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Khatun AA, Muthanna YA, Punetha N, Jafri HH. Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states. Phys Rev E 2024; 109:034208. [PMID: 38632727 DOI: 10.1103/physreve.109.034208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2022] [Accepted: 02/05/2024] [Indexed: 04/19/2024]
Abstract
We study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. For analysis, we first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors. Consequently, different oscillators may show a dynamics that is intermittently synchronized (or desynchronized), giving rise to intermittent chimera states. The behavior of the intermittent laminar phases is characterized by the characteristic time spent in the synchronization manifold, which decays as a power law. Such intermittent dynamics is quite general and is also observed in an ensemble of a large number of oscillators arranged in variety of network topologies including nonlocal, scale-free, random, and small-world networks.
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Affiliation(s)
- Anjuman Ara Khatun
- Department of Physics, Aligarh Muslim University, Aligarh 202 002, India
- Department of Physics, Indian Institute of Technology Bombay, Mumbai 400 076, India
| | - Yusra Ahmed Muthanna
- Department of Physics, Aligarh Muslim University, Aligarh 202 002, India
- Physics Department, Taiz University, Taiz 6803, Yemen
| | | | - Haider Hasan Jafri
- Department of Physics, Aligarh Muslim University, Aligarh 202 002, India
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Yan J, Majumdar M, Ruffo S, Sato Y, Beck C, Klages R. Transition to anomalous dynamics in a simple random map. CHAOS (WOODBURY, N.Y.) 2024; 34:023128. [PMID: 38377287 DOI: 10.1063/5.0176310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 01/15/2024] [Indexed: 02/22/2024]
Abstract
The famous doubling map (or dyadic transformation) is perhaps the simplest deterministic dynamical system exhibiting chaotic dynamics. It is a piecewise linear time-discrete map on the unit interval with a uniform slope larger than one, hence expanding, with a positive Lyapunov exponent and a uniform invariant density. If the slope is less than one, the map becomes contracting, the Lyapunov exponent is negative, and the density trivially collapses onto a fixed point. Sampling from these two different types of maps at each time step by randomly selecting the expanding one with probability p, and the contracting one with probability 1-p, gives a prototype of a random dynamical system. Here, we calculate the invariant density of this simple random map, as well as its position autocorrelation function, analytically and numerically under variation of p. We find that the map exhibits a non-trivial transition from fully chaotic to completely regular dynamics by generating a long-time anomalous dynamics at a critical sampling probability pc, defined by a zero Lyapunov exponent. This anomalous dynamics is characterized by an infinite invariant density, weak ergodicity breaking, and power-law correlation decay.
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Affiliation(s)
- Jin Yan
- Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany and Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
| | - Moitrish Majumdar
- Department of Applied Mathematics, University of California, Merced, 5200 N. Lake Road, Merced, California 95343, USA
| | - Stefano Ruffo
- SISSA, Via Bonomea 265, 34136 Trieste, Italy; INFN Sezione di Trieste, via Valerio 2, 34127 Trieste, Italy; and Istituto dei Sistemi Complessi, via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy
| | - Yuzuru Sato
- RIES/Department of Mathematics, Hokkaido University, N12 W7 Kita-ku, Sapporo 0600812, Hokkaido, Japan
- London Mathematical Laboratory, 8 Margravine Gardens, London W6 8RH, United Kingdom
| | - Christian Beck
- School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
- The Alan Turing Institute, 96 Euston Road, London NW1 2DB, United Kingdom
| | - Rainer Klages
- London Mathematical Laboratory, 8 Margravine Gardens, London W6 8RH, United Kingdom
- School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
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3
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Wang Y, Wang L, Fan H, Ma J, Cao H, Wang X. Breathing cluster in complex neuron-astrocyte networks. CHAOS (WOODBURY, N.Y.) 2023; 33:113118. [PMID: 37967261 DOI: 10.1063/5.0146906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Accepted: 10/20/2023] [Indexed: 11/17/2023]
Abstract
Brain activities are featured by spatially distributed neural clusters of coherent firings and a spontaneous slow switching of the clusters between the coherent and incoherent states. Evidences from recent in vivo experiments suggest that astrocytes, a type of glial cell regarded previously as providing only structural and metabolic supports to neurons, participate actively in brain functions by regulating the neural firing activities, yet the underlying mechanism remains unknown. Here, introducing astrocyte as a reservoir of the glutamate released from the neuron synapses, we propose the model of the complex neuron-astrocyte network, and investigate the roles of astrocytes in regulating the cluster synchronization behaviors of networked chaotic neurons. It is found that a specific set of neurons on the network are synchronized and form a cluster, while the remaining neurons are kept as desynchronized. Moreover, during the course of network evolution, the cluster is switching between the synchrony and asynchrony states in an intermittent fashion, henceforth the phenomenon of "breathing cluster." By the method of symmetry-based analysis, we conduct a theoretical investigation on the synchronizability of the cluster. It is revealed that the contents of the cluster are determined by the network symmetry, while the breathing of the cluster is attributed to the interplay between the neural network and the astrocyte. The phenomenon of breathing cluster is demonstrated in different network models, including networks with different sizes, nodal dynamics, and coupling functions. The findings shed light on the cellular mechanism of astrocytes in regulating neural activities and give insights into the state-switching of the neocortex.
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Affiliation(s)
- Ya Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Liang Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Huawei Fan
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
| | - Jun Ma
- Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
| | - Hui Cao
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Xingang Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
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4
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Kong LW, Lai YC. Short-lived chimera states. CHAOS (WOODBURY, N.Y.) 2023; 33:2894496. [PMID: 37276573 DOI: 10.1063/5.0145573] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2023] [Accepted: 04/21/2023] [Indexed: 06/07/2023]
Abstract
In the classic Kuramoto system of coupled two-dimensional rotators, chimera states characterized by the coexistence of synchronous and asynchronous groups of oscillators are long-lived because the average lifetime of these states increases exponentially with the system size. Recently, it was discovered that, when the rotators in the Kuramoto model are three-dimensional, the chimera states become short-lived in the sense that their lifetime scales with only the logarithm of the dimension-augmenting perturbation. We introduce transverse-stability analysis to understand the short-lived chimera states. In particular, on the unit sphere representing three-dimensional (3D) rotations, the long-lived chimera states in the classic Kuramoto system occur on the equator, to which latitudinal perturbations that make the rotations 3D are transverse. We demonstrate that the largest transverse Lyapunov exponent calculated with respect to these long-lived chimera states is typically positive, making them short-lived. The transverse-stability analysis turns the previous numerical scaling law of the transient lifetime into an exact formula: the "free" proportional constant in the original scaling law can now be precisely determined in terms of the largest transverse Lyapunov exponent. Our analysis reinforces the speculation that in physical systems, chimera states can be short-lived as they are vulnerable to any perturbations that have a component transverse to the invariant subspace in which they live.
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Affiliation(s)
- Ling-Wei Kong
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
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5
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Müller-Bender D, Valani RN, Radons G. Pseudolaminar chaos from on-off intermittency. Phys Rev E 2023; 107:014208. [PMID: 36797907 DOI: 10.1103/physreve.107.014208] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2022] [Accepted: 01/03/2023] [Indexed: 06/18/2023]
Abstract
In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)0031-900710.1103/PhysRevLett.128.074101] known from delay systems with lag-time modulation. Applying, however, to such systems a test for laminar chaos, as proposed in [Phys. Rev. E 101, 032213 (2020)2470-004510.1103/PhysRevE.101.032213], these signals fail such a test, thus leading to the notion of pseudolaminar chaos. The latter can be interpreted as integrated periodically driven on-off intermittency. We demonstrate that, on a signal level, true laminar and pseudolaminar chaos are hardly distinguishable in systems with and without dynamical noise. However, very pronounced differences become apparent when correlations of signals and increments are considered. We compare and contrast these properties of pseudolaminar chaos with true laminar chaos.
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Affiliation(s)
- David Müller-Bender
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Rahil N Valani
- School of Mathematical Sciences, University of Adelaide, Adelaide, South Australia 5005, Australia
| | - Günter Radons
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
- ICM - Institute for Mechanical and Industrial Engineering, 09117 Chemnitz, Germany
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Analysis of the Type V Intermittency Using the Perron-Frobenius Operator. Symmetry (Basel) 2022. [DOI: 10.3390/sym14122519] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022] Open
Abstract
A methodology to study the reinjection process in type V intermittency is introduced. The reinjection probability density function (RPD), and the probability density of the laminar lengths (RPDL) for type V intermittency are calculated. A family of maps with discontinuous and continuous RPD functions is analyzed. Several tests were performed, in which the proposed technique was compared with the classical theory of intermittency, the M function methodology, and numerical data. The analysis exposed that the new technique can accurately capture the numerical data. Therefore, the scheme presented herein is a useful tool to theoretically evaluate the statistical variables for type V intermittency.
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7
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Song Y, Witten TA. Stochastic synchronization induced by noise. Phys Rev E 2022; 106:044207. [PMID: 36397484 DOI: 10.1103/physreve.106.044207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture. The copies differ only in their arbitrary phases ϕ. Weak, randomly timed external impulses applied to all the copies can synchronize these phases over time. Beyond a threshold strength there is no such convergence to a common phase. Instead, the synchronization becomes erratic: successive impulses produce stochastic fluctuations in the phase distribution q(ϕ), ranging from near-perfect to near-random synchronization. Here we show that the sampled entropies of these phase distributions themselves form a steady-state ensemble, whose average can be made arbitrarily negative by tuning the impulse strength. A random-walk description of the entropy's evolution accounts for the observed exponential distribution of entropies and for the stochastic synchronization phenomenon.
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Affiliation(s)
- Yunxiang Song
- Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Thomas A Witten
- Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
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8
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Martinez-Saito M. Discrete scaling and criticality in a chain of adaptive excitable integrators. CHAOS, SOLITONS & FRACTALS 2022; 163:112574. [DOI: 10.1016/j.chaos.2022.112574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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9
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Galuzio PP, Cherif A, Tao X, Thwin O, Zhang H, Thijssen S, Kotanko P. Identification of arterial oxygen intermittency in oximetry data. Sci Rep 2022; 12:16023. [PMID: 36163364 PMCID: PMC9511470 DOI: 10.1038/s41598-022-20493-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 09/14/2022] [Indexed: 11/09/2022] Open
Abstract
In patients with kidney failure treated by hemodialysis, intradialytic arterial oxygen saturation (SaO2) time series present intermittent high-frequency high-amplitude oximetry patterns (IHHOP), which correlate with observed sleep-associated breathing disturbances. A new method for identifying such intermittent patterns is proposed. The method is based on the analysis of recurrence in the time series through the quantification of an optimal recurrence threshold ([Formula: see text]). New time series for the value of [Formula: see text] were constructed using a rolling window scheme, which allowed for real-time identification of the occurrence of IHHOPs. The results for the optimal recurrence threshold were confronted with standard metrics used in studies of obstructive sleep apnea, namely the oxygen desaturation index (ODI) and oxygen desaturation density (ODD). A high correlation between [Formula: see text] and the ODD was observed. Using the value of the ODI as a surrogate to the apnea-hypopnea index (AHI), it was shown that the value of [Formula: see text] distinguishes occurrences of sleep apnea with great accuracy. When subjected to binary classifiers, this newly proposed metric has great power for predicting the occurrences of sleep apnea-related events, as can be seen by the larger than 0.90 AUC observed in the ROC curve. Therefore, the optimal threshold [Formula: see text] from recurrence analysis can be used as a metric to quantify the occurrence of abnormal behaviors in the arterial oxygen saturation time series.
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Affiliation(s)
- Paulo P Galuzio
- Research Division, Renal Research Institute, New York, NY, USA.
| | - Alhaji Cherif
- Research Division, Renal Research Institute, New York, NY, USA.
| | - Xia Tao
- Research Division, Renal Research Institute, New York, NY, USA
| | - Ohnmar Thwin
- Research Division, Renal Research Institute, New York, NY, USA
| | - Hanjie Zhang
- Research Division, Renal Research Institute, New York, NY, USA
| | | | - Peter Kotanko
- Research Division, Renal Research Institute, New York, NY, USA.,Icahn School of Medicine at Mount Sinai Health System, New York, NY, USA
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10
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Vissio G, Provenzale A. On-off intermittency and irruptions in host-parasitoid dynamics. J Theor Biol 2022; 546:111174. [DOI: 10.1016/j.jtbi.2022.111174] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2021] [Revised: 05/02/2022] [Accepted: 05/19/2022] [Indexed: 10/18/2022]
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11
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Abstract
Just below a Period-3 window, the logistic map exhibits intermittency. Then, the third iterate of this map has been widely used to explain the chaotic intermittency concept. Much attention has been paid to describing the behavior around the vanished fixed points, the tangent bifurcation, and the formation of the characteristic channel between the map and the diagonal for type-I intermittency. However, the reinjection mechanism has not been deeply analyzed. In this paper, we studied the reinjection processes for the three fixed points around which intermittency is generated. We calculated the reinjection probability density function, the probability density of the laminar lengths, and the characteristic relation. We found that the reinjection mechanisms have broader behavior than the usually used uniform reinjection. Furthermore, the reinjection processes depend on the fixed point.
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12
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Goodfellow M, Andrzejak RG, Masoller C, Lehnertz K. What Models and Tools can Contribute to a Better Understanding of Brain Activity? FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:907995. [PMID: 36926061 PMCID: PMC10013030 DOI: 10.3389/fnetp.2022.907995] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 06/06/2022] [Indexed: 12/18/2022]
Abstract
Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.
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Affiliation(s)
- Marc Goodfellow
- Living Systems Institute, University of Exeter, Exeter, United Kingdom
| | - Ralph G Andrzejak
- Department of Information and Communication Technologies, University Pompeu Fabra, Barcelona, Spain
| | - Cristina Masoller
- Department of Physics, Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany.,Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
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13
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Ge P, Cao H. Intermittent evolution routes to the periodic or the chaotic orbits in Rulkov map. CHAOS (WOODBURY, N.Y.) 2021; 31:093119. [PMID: 34598445 DOI: 10.1063/5.0060205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 09/07/2021] [Indexed: 06/13/2023]
Abstract
This paper concerns the intermittent evolution routes to the asymptotic regimes in the Rulkov map. That is, the windows with transient approximate periodic and transient chaotic behaviors occur alternatively before the system reaches the periodic or the chaotic orbits. Meanwhile, the evolution routes to chaotic orbits can be classified into different types according to the windows before reaching asymptotic chaotic states. In addition, the initial values can be regarded as a key factor affecting the asymptotic behaviors and the evolution routes. The effects of the initial values are given by parameter planes, bifurcation diagrams, and waveforms. In order to investigate whether the intermittent evolution routes can be learned by machine learning, some experiments are given to understanding the differences between the trajectories of the Rulkov map generated by the numerical simulations and predicted by the neural networks. These results show that there is about 60% accuracy rate of successfully predicting both the evolution routes and the asymptotic period-3 orbits using a three-layer feedforward neural network, while the bifurcation diagrams can be reconstructed using reservoir computing except a few parameter conditions.
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Affiliation(s)
- Penghe Ge
- Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People's Republic of China
| | - Hongjun Cao
- Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People's Republic of China
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Alicki R, Gelbwaser-Klimovsky D, Jenkins A. The Problem of Engines in Statistical Physics. ENTROPY 2021; 23:e23081095. [PMID: 34441235 PMCID: PMC8391344 DOI: 10.3390/e23081095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Revised: 07/31/2021] [Accepted: 08/12/2021] [Indexed: 11/16/2022]
Abstract
Engines are open systems that can generate work cyclically at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their dynamics in time a theoretical blind spot. This has hampered the usefulness of statistical mechanics applied to active systems, including living matter. We argue that recent advances in the theory of open quantum systems, coupled with renewed interest in understanding how active forces result from positive feedback between different macroscopic degrees of freedom in the presence of dissipation, point to a more realistic description of autonomous engines. We propose a general conceptualization of an engine that helps clarify the distinction between its heat and work outputs. Based on this, we show how the external loading force and the thermal noise may be incorporated into the relevant equations of motion. This modifies the usual Fokker-Planck and Langevin equations, offering a thermodynamically complete formulation of the irreversible dynamics of simple oscillating and rotating engines.
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Affiliation(s)
- Robert Alicki
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland;
| | - David Gelbwaser-Klimovsky
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;
| | - Alejandro Jenkins
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland;
- Laboratorio de Física Teórica y Computacional, Escuela de Física, Universidad de Costa Rica, San José 11501-2060, Costa Rica
- Correspondence:
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Abstract
The environment affects population dynamics through multiple drivers. Here we explore a simplified version of such influence in a three-species food chain, making use of the Hastings–Powell model. This represents an idealized resource–consumer–predator chain, or equivalently, a vegetation–host–parasitoid system. By stochastically perturbing the value of some parameters in this dynamical system, we observe dramatic modifications in the system behavior. In particular, we show the emergence of on–off intermittency, i.e., an irregular alternation between stable phases and sudden bursts in population size, which hints towards a possible conceptual description of population outbursts grounded into an environment-driven mechanism.
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Calculation of the Statistical Properties in Intermittency Using the Natural Invariant Density. Symmetry (Basel) 2021. [DOI: 10.3390/sym13060935] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
We use the natural invariant density of the map and the Perron–Frobenius operator to analytically evaluate the statistical properties for chaotic intermittency. This study can be understood as an improvement of the previous ones because it does not introduce assumptions about the reinjection probability density function in the laminar interval or the map density at pre-reinjection points. To validate the new theoretical equations, we study a symmetric map and a non-symmetric one. The cusp map has symmetry about x=0, but the Manneville map has no symmetry. We carry out several comparisons between the theoretical equations here presented, the M function methodology, the classical theory of intermittency, and numerical data. The new theoretical equations show more accuracy than those calculated with other techniques.
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17
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van Kan A, Alexakis A, Brachet ME. Lévy on-off intermittency. Phys Rev E 2021; 103:052115. [PMID: 34134220 DOI: 10.1103/physreve.103.052115] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 04/27/2021] [Indexed: 11/07/2022]
Abstract
We present an alternative form of intermittency, Lévy on-off intermittency, which arises from multiplicative α-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation. We characterize the system in the parameter space (α,β) of the noise, with stability parameter α∈(0,2) and skewness parameter β∈[-1,1]. Five regimes are identified in this parameter space, in addition to the well-studied Gaussian case α=2. Three regimes are located at 1<α<2, where the noise has finite mean but infinite variance. They are differentiated by β and all display a critical transition at the deterministic instability threshold, with on-off intermittency close to onset. Critical exponents are computed from the stationary distribution. Each regime is characterized by a specific form of the density and specific critical exponents, which differ starkly from the Gaussian case. A finite or infinite number of integer-order moments may converge, depending on parameters. Two more regimes are found at 0<α≤1. There, the mean of the noise diverges, and no critical transition occurs. In one case, the origin is always unstable, independently of the distance μ from the deterministic threshold. In the other case, the origin is conversely always stable, independently of μ. We thus demonstrate that an instability subject to nonequilibrium, power-law-distributed fluctuations can display substantially different properties than for Gaussian thermal fluctuations, in terms of statistics and critical behavior.
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Affiliation(s)
- Adrian van Kan
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Alexandros Alexakis
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Marc-Etienne Brachet
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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van Kan A, Alexakis A, Brachet ME. Intermittency of three-dimensional perturbations in a point-vortex model. Phys Rev E 2021; 103:053102. [PMID: 34134270 DOI: 10.1103/physreve.103.053102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 04/28/2021] [Indexed: 11/07/2022]
Abstract
Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based on known physical properties of such 3D instabilities, we propose a simple, energy-conserving model describing this situation. It consists of a regularized 2D point-vortex flow coupled to localized 3D perturbations ("ergophages"), such that ergophages can gain energy by altering vortex-vortex distances through an induced divergent velocity field, thus decreasing point-vortex energy. We investigate the model in three distinct stages of evolution: (i) The linear regime, where the amplitude of the ergophages grows or decays exponentially on average, with an instantaneous growth rate that fluctuates randomly in time. The instantaneous growth rate has a small auto-correlation time, and a probability distribution featuring a power-law tail with exponent between -2 and -5/3 (up to a cutoff) depending on the point-vortex base flow. Consequently, the logarithm of the ergophage amplitude performs a Lévy flight. (ii) The passive-nonlinear regime of the model, where the 2D flow evolves independently of the ergophage amplitudes, which saturate by non-linear self-interactions without affecting the 2D flow. In this regime the system exhibits a new type of on-off intermittency that we name Lévy on-off intermittency, which we define and study in a companion paper [van Kan et al., Phys. Rev. E 103, 052115 (2021)1063-651X10.1103/PhysRevE.103.052115]. We compute the bifurcation diagram for the mean and variance of the perturbation amplitude, as well as the probability density of the perturbation amplitude. (iii) Finally, we characterize the fully nonlinear regime, where ergophages feed back on the 2D flow, and study how the vortex temperature is altered by the interaction with ergophages. It is shown that when the amplitude of the ergophages is sufficiently large, the condensate is disrupted and the 2D flow saturates to a zero-temperature state. Given the limitations of existing theories, our model provides a new perspective on 3D instabilities growing on 2D flows, which will be useful in analyzing and understanding the much more complex results of DNS and potentially guide further theoretical developments.
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Affiliation(s)
- Adrian van Kan
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Alexandros Alexakis
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Marc-Etienne Brachet
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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19
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Sano K, Mitsui T, Akimoto T. Reduction of the synchronization time in random logistic maps. Phys Rev E 2021; 102:062209. [PMID: 33466000 DOI: 10.1103/physreve.102.062209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2020] [Accepted: 11/15/2020] [Indexed: 11/07/2022]
Abstract
We report on the effects of additive noises in a nonchaotic logistic map. In this system, the Lyapunov exponent changes from negative to positive as the noise intensity is increased. When the Lyapunov exponent is negative, the synchronization of orbits with different initial conditions occurs. We find that the synchronization time cannot be determined solely by the Lyapunov exponent when the noise intensity is greater than a point at which the Lyapunov exponent is minimum. We show that this reduction of the synchronization time is attributed to initial nonstationary behaviors, where the critical point of the logistic map plays an important role.
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Affiliation(s)
- Kaito Sano
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Kashiwa 277-8561, Japan
| | - Takahito Mitsui
- Department of Mathematics and Computer Science, Free University Berlin, Arnimallee 6, Berlin 14195, Germany.,Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam 14473, Germany
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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20
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Detection of embedded dynamics in the Györgyi-Field model. Sci Rep 2020; 10:21030. [PMID: 33273551 PMCID: PMC7713133 DOI: 10.1038/s41598-020-77874-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Accepted: 11/11/2020] [Indexed: 11/08/2022] Open
Abstract
The main aim of this paper is to detect embedded dynamics of the Györgyi-Field model of the Belousov-Zhabotinsky chemical reaction. The corresponding three-variable model given as a set of nonlinear ordinary differential equations depends on one parameter, the flow rate. As certain values of this parameter can give rise to chaos, an analysis was performed in order to identify different dynamics regimes. Dynamical properties were qualified and quantified using classical and also new techniques; namely, phase portraits, bifurcation diagrams, the Fourier spectra analysis, the 0-1 test for chaos, approximate entropy, and the maximal Lyapunov exponent. The correlation between approximate entropy and the 0-1 test for chaos was observed and described in detail. The main discovery was that the three-stage system of nested sub-intervals of flow rates showed the same pattern in the 0-1 test for chaos and approximate entropy at every level. The investigation leads to the open problem of whether the set of flow rate parameters has Cantor-like structure.
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21
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Alberti T, Consolini G, Ditlevsen PD, Donner RV, Quattrociocchi V. Multiscale measures of phase-space trajectories. CHAOS (WOODBURY, N.Y.) 2020; 30:123116. [PMID: 33380062 DOI: 10.1063/5.0008916] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 11/12/2020] [Indexed: 06/12/2023]
Abstract
Characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series is one of the most intensively studied contemporary problems in nonlinear sciences. In this work, we address this problem by combining two established concepts-empirical mode decomposition (EMD) and generalized fractal dimensions-into a unified analysis framework. Specifically, we demonstrate that the intrinsic mode functions derived by EMD can be used as a source of local (in terms of scales) information about the properties of the phase-space trajectory of the system under study, allowing us to derive multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales. This formalism is applied to three well-known low-dimensional deterministic dynamical systems (the Hénon map, the Lorenz '63 system, and the standard map), three realizations of fractional Brownian motion with different Hurst exponents, and two somewhat higher-dimensional deterministic dynamical systems (the Lorenz '96 model and the on-off intermittency model). These examples allow us to assess the performance of our formalism with respect to practically relevant aspects like additive noise, different initial conditions, the length of the time series under study, low- vs high-dimensional dynamics, and bursting effects. Finally, by taking advantage of two real-world systems whose multiscale features have been widely investigated (a marine stack record providing a proxy of the global ice volume variability of the past 5×106 years and the SYM-H geomagnetic index), we also illustrate the applicability of this formalism to real-world time series.
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Affiliation(s)
- Tommaso Alberti
- INAF-Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Roma, Italy
| | - Giuseppe Consolini
- INAF-Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Roma, Italy
| | - Peter D Ditlevsen
- Centre for Ice and Climate, Niels Bohr Institute, University of Copenhagen, Copenhagen 2200, Denmark
| | - Reik V Donner
- Department of Water, Environment, Construction and Safety, Magdeburg-Stendal University of Applied Sciences, Breitscheidstraße 2, 39114 Magdeburg, Germany
| | - Virgilio Quattrociocchi
- INAF-Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Roma, Italy
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22
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Koronovskii AA, Moskalenko OI, Pivovarov AA, Evstifeev EV. Intermittent route to generalized synchronization in bidirectionally coupled chaotic oscillators. CHAOS (WOODBURY, N.Y.) 2020; 30:083133. [PMID: 32872830 DOI: 10.1063/5.0007156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2020] [Accepted: 08/03/2020] [Indexed: 06/11/2023]
Abstract
The type of transition from asynchronous behavior to the generalized synchronization regime in mutually coupled chaotic oscillators has been studied. To separate the epochs of the synchronous and asynchronous motion in time series of mutually coupled chaotic oscillators, a method based on the local Lyapunov exponent calculation has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled dynamical systems for which the type of transition is well known. The transition to generalized synchronization regime in mutually coupled systems has been shown to be an on-off intermittency as well as in the case of the unidirectional coupling.
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Affiliation(s)
- Alexey A Koronovskii
- Faculty of Nonlinear Processes, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia
| | - Olga I Moskalenko
- Faculty of Nonlinear Processes, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia
| | - Anatoliy A Pivovarov
- Faculty of Nonlinear Processes, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia
| | - Evgeniy V Evstifeev
- Faculty of Nonlinear Processes, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia
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23
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Koronovskii AA, Moskalenko OI, Pivovarov AA, Khanadeev VA, Hramov AE, Pisarchik AN. Jump intermittency as a second type of transition to and from generalized synchronization. Phys Rev E 2020; 102:012205. [PMID: 32794947 DOI: 10.1103/physreve.102.012205] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Accepted: 06/18/2020] [Indexed: 11/07/2022]
Abstract
The transition from asynchronous dynamics to generalized chaotic synchronization and then to completely synchronous dynamics is known to be accompanied by on-off intermittency. We show that there is another (second) type of the transition called jump intermittency which occurs near the boundary of generalized synchronization in chaotic systems with complex two-sheeted attractors. Although this transient behavior also exhibits intermittent dynamics, it differs sufficiently from on-off intermittency supposed hitherto to be the only type of motion corresponding to the transition to generalized synchronization. This type of transition has been revealed and the underling mechanism has been explained in both unidirectionally and mutually coupled chaotic Lorenz and Chen oscillators. To detect the epochs of synchronous and asynchronous motion in mutually coupled oscillators with complex topology of an attractor a technique based on finding time intervals when the phase trajectories are located on equal or different sheets of chaotic attractors of coupled oscillators has been developed. We have also shown that in the unidirectionally coupled systems the proposed technique gives the same results that may obtained with the help of the traditional method using the auxiliary system approach.
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Affiliation(s)
- Alexey A Koronovskii
- Saratov State University, 83 Astrakhanskaya Strasse, 410012 Saratov, Russia and Regional Scientific and Educational Mathematical Center "Mathematics of Future Technologies," 410012, Saratov, Russia
| | - Olga I Moskalenko
- Saratov State University, 83 Astrakhanskaya Strasse, 410012 Saratov, Russia and Regional Scientific and Educational Mathematical Center "Mathematics of Future Technologies," 410012, Saratov, Russia
| | - Anatolii A Pivovarov
- Saratov State University, 83 Astrakhanskaya Strasse, 410012 Saratov, Russia and Regional Scientific and Educational Mathematical Center "Mathematics of Future Technologies," 410012, Saratov, Russia
| | - Vladislav A Khanadeev
- Saratov State University, 83 Astrakhanskaya Strasse, 410012 Saratov, Russia and Regional Scientific and Educational Mathematical Center "Mathematics of Future Technologies," 410012, Saratov, Russia
| | - Alexander E Hramov
- Innopolis University, 1 Universitetskaya Strasse, 420500 Innopolis, Russia
| | - Alexander N Pisarchik
- Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcón, Madrid, Spain
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24
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Bordbar P, Ahadpour S. Type-I intermittency from Markov binary block visibility graph perspective. J Appl Stat 2020; 48:1303-1318. [DOI: 10.1080/02664763.2020.1761949] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Pejman Bordbar
- Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran
| | - Sodeif Ahadpour
- Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran
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25
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Guseva K, Feudel U. Numerical modelling of the effect of intermittent upwelling events on plankton blooms. J R Soc Interface 2020; 17:20190889. [PMID: 32343934 DOI: 10.1098/rsif.2019.0889] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In the marine environment, biological processes are strongly affected by oceanic currents, particularly by eddies (vortices) formed by the hydrodynamic flow field. Employing a kinematic flow field coupled to a population dynamical model for plankton growth, we study the impact of an intermittent upwelling of nutrients on triggering harmful algal blooms (HABs). Though it is widely believed that additional nutrients boost the formation of HABs or algal blooms in general, we show that the response of the plankton to nutrient plumes depends crucially on the mesoscale hydrodynamic flow structure. In general, nutrients can either be quickly washed out from the observation area, or can be captured by the vortices in the flow. The occurrence of either scenario depends on the relation between the time scales of the vortex formation and nutrient upwelling as well as the time instants at which upwelling pulses occur and how long they last. We show that these two scenarios result in very different responses in plankton dynamics which makes it very difficult to predict whether nutrient upwelling will lead to a HAB or not. This may in part explain why observational data are sometimes inconclusive in establishing a connection between upwelling events and plankton blooms.
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Affiliation(s)
- Ksenia Guseva
- Department of Microbiology and Ecosystem Science, University of Vienna, Vienna, Austria.,Theoretical Physics/Complex Systems, ICBM, University of Oldenburg, 26129 Oldenburg, Germany
| | - Ulrike Feudel
- Theoretical Physics/Complex Systems, ICBM, University of Oldenburg, 26129 Oldenburg, Germany
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26
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Tokami T, Hachijo T, Miyano T, Gotoda H. Spatiotemporal dynamics of a buoyancy-driven turbulent fire. Phys Rev E 2020; 101:042214. [PMID: 32422785 DOI: 10.1103/physreve.101.042214] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Accepted: 03/14/2020] [Indexed: 06/11/2023]
Abstract
We numerically study the spatiotemporal dynamics and predictability of a buoyancy-driven turbulent fire. A significant transition from order to disorder structures can be observed from the mean degree in the spatial horizontal visibility graph. The gravitational term (baroclinic torque term) in the vorticity equation has a significant impact on the formation of the order (disorder) structure in the near field (far field). The entropy flow transport from temperature to flow velocity fluctuations is predominant near the interface between hot combustion products and ambient air. The transfer entropy is an important measure for determining the predictability of flow velocity fluctuations in the near field obtained by reservoir computing.
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Affiliation(s)
- Takumi Tokami
- Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
| | - Takayoshi Hachijo
- Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
| | - Takaya Miyano
- Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan
| | - Hiroshi Gotoda
- Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
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27
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Ibbeken G, Green G, Wilczek M. Large-Scale Pattern Formation in the Presence of Small-Scale Random Advection. PHYSICAL REVIEW LETTERS 2019; 123:114501. [PMID: 31573241 DOI: 10.1103/physrevlett.123.114501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Indexed: 06/10/2023]
Abstract
Despite the presence of strong fluctuations, many turbulent systems such as Rayleigh-Bénard convection and Taylor-Couette flow display self-organized large-scale flow patterns. How do small-scale turbulent fluctuations impact the emergence and stability of such large-scale flow patterns? Here, we approach this question conceptually by investigating a class of pattern forming systems in the presence of random advection by a Kraichnan-Kazantsev velocity field. Combining tools from pattern formation with statistical theory and simulations, we show that random advection shifts the onset and the wave number of emergent patterns. As a simple model for pattern formation in convection, the effects are demonstrated with a generalized Swift-Hohenberg equation including random advection. We also discuss the implications of our results for the large-scale flow of turbulent Rayleigh-Bénard convection.
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Affiliation(s)
- Gregor Ibbeken
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Am Faßberg 17, 37077 Göttingen, Germany
- Faculty of Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Gerrit Green
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Am Faßberg 17, 37077 Göttingen, Germany
- Faculty of Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Michael Wilczek
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Am Faßberg 17, 37077 Göttingen, Germany
- Faculty of Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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28
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Belyaev IA, Biryukov DA, Gerasimov DN, Yurin EI. On-off intermittency and hard turbulence in the flow of fluid in the magnetic field. CHAOS (WOODBURY, N.Y.) 2019; 29:083119. [PMID: 31472485 DOI: 10.1063/1.5098538] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2019] [Accepted: 07/25/2019] [Indexed: 06/10/2023]
Abstract
This work provides an analysis of experiments in which various modes of mercury flow in a constant external magnetic field were observed; we examined the temperature oscillations in the mercury flow in a heated pipe at various Reynolds and Hartmann numbers. In some modes, the temperature oscillations have specific forms of strong aperiodic "bursts" over the weak irregular background, which are specific to the developed turbulent flow. To determine the nature of these temperature oscillations and the characteristics of the fluid flow, we examined them through the apparatus of nonlinear dynamics. The totality of all the results (autocorrelation function, correlation integral, maximum Lyapunov exponents, and Fourier transform) provide evidence of the chaotic nature of the observed flow modes despite the relative weakness of high-frequency harmonics in comparison to low-frequency ones. In the case of separate bursts of turbulence, the duration of the laminar phase τ follows the known distribution ∼τ-3/2, derived from the theory of on-off intermittency.
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Affiliation(s)
- I A Belyaev
- Joint Institute for High Temperatures RAS, Izhorskaya, 13-2, Moscow 125412, Russia
| | - D A Biryukov
- Joint Institute for High Temperatures RAS, Izhorskaya, 13-2, Moscow 125412, Russia
| | - D N Gerasimov
- National Research University "Moscow Power Engineering Institute", Krasnokazarmennaya, 17, Moscow 111250, Russia
| | - E I Yurin
- National Research University "Moscow Power Engineering Institute", Krasnokazarmennaya, 17, Moscow 111250, Russia
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29
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Sato Y, Klages R. Anomalous Diffusion in Random Dynamical Systems. PHYSICAL REVIEW LETTERS 2019; 122:174101. [PMID: 31107078 DOI: 10.1103/physrevlett.122.174101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Revised: 02/13/2019] [Indexed: 06/09/2023]
Abstract
Consider a chaotic dynamical system generating diffusionlike Brownian motion. Consider a second, nonchaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in time. What type of diffusion is exhibited by this random dynamical system? We show that the resulting dynamics can generate anomalous diffusion, where in contrast to Brownian normal diffusion the mean square displacement of an ensemble of particles increases nonlinearly in time. Randomly mixing simple deterministic walks on the line, we find anomalous dynamics characterized by aging, weak ergodicity breaking, breaking of self-averaging, and infinite invariant densities. This result holds for general types of noise and for perturbing nonlinear dynamics in bifurcation scenarios.
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Affiliation(s)
- Yuzuru Sato
- RIES/Department of Mathematics, Hokkaido University, N20 W10 Kita-ku, Sapporo, 0010020 Hokkaido, Japan
- London Mathematical Laboratory, 14 Buckingham Street, London WC2N 6DF, United Kingdom
| | - Rainer Klages
- Queen Mary University of London, School of Mathematical Sciences, Mile End Road, London E1 4NS, United Kingdom
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
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30
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Raaj A, Venkatramani J, Mondal S. Synchronization of pitch and plunge motions during intermittency route to aeroelastic flutter. CHAOS (WOODBURY, N.Y.) 2019; 29:043129. [PMID: 31042932 DOI: 10.1063/1.5084719] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2018] [Accepted: 04/05/2019] [Indexed: 06/09/2023]
Abstract
Interaction of fluid forces with flexible structures is often prone to dynamical instabilities, such as aeroelastic flutter. The onset of this instability is marked by sustained large amplitude oscillations and is detrimental to the structure's integrity. Therefore, investigating the possible physical mechanisms behind the onset of flutter instability has attracted considerable attention within the aeroelastic community. Recent studies have shown that in the presence of oncoming fluctuating flows, the onset of flutter instability is presaged by an intermediate regime of oscillations called intermittency. Further, based on the intensity of flow fluctuations and the relative time scales present in the flow, qualitatively different types of intermittency at different flow regimes have been reported hitherto. However, the coupled interaction between the pitch (torsion) and plunge (bending) modes during the transition to aeroelastic flutter has not been explored. With this, we demonstrate with a mathematical model that the onset of flutter instability under randomly fluctuating flows occurs via a mutual phase synchronization between the pitch and the plunge modes. We show that at very low values of mean flow speeds, the response is by and large noisy and, consequently, a phase asynchrony between the modes is present. Interestingly, during the regime of intermittency, we observe the coexistence of patches of synchronized periodic bursts interspersed amidst a state of desynchrony between the pitch and the plunge modes. On the other hand, at the onset of flutter, we observe a complete phase synchronization between the pitch and plunge modes. This study concludes by utilizing phase locking value as a quantitative measure to demarcate different states of synchronization in the aeroelastic response.
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Affiliation(s)
- Ashwad Raaj
- Department of Mechanical Engineering, Shiv Nadar University, Greater Noida 201314, India
| | - J Venkatramani
- Department of Mechanical Engineering, Shiv Nadar University, Greater Noida 201314, India
| | - Sirshendu Mondal
- Department of Mechanical Engineering, National Institute of Technology, Durgapur 713209, India
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31
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Saiki Y, Sanjuán MAF, Yorke JA. Low-dimensional paradigms for high-dimensional hetero-chaos. CHAOS (WOODBURY, N.Y.) 2018; 28:103110. [PMID: 30384627 DOI: 10.1063/1.5045693] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2018] [Accepted: 09/26/2018] [Indexed: 06/08/2023]
Abstract
The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two such regions and each contains trajectories that stay in the region for all time-while typical trajectories wander throughout the attractor. Furthermore, if arbitrarily close to each point of the attractor there are points on periodic orbits that have different unstable dimensions, then we say such an attractor is "hetero-chaotic" (i.e., it has heterogeneous chaos). This is hard to picture but we believe that most physical systems possessing a high-dimensional attractor are of this type. We have created simplified models with that behavior to give insight into real high-dimensional phenomena.
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Affiliation(s)
- Yoshitaka Saiki
- Graduate School of Business Administration, Hitotsubashi University, Tokyo 186-8601, Japan
| | - Miguel A F Sanjuán
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - James A Yorke
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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32
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Perrard S, Labousse M. Transition to chaos in wave memory dynamics in a harmonic well: Deterministic and noise-driven behavior. CHAOS (WOODBURY, N.Y.) 2018; 28:096109. [PMID: 30278648 DOI: 10.1063/1.5032088] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2018] [Accepted: 08/22/2018] [Indexed: 06/08/2023]
Abstract
A walker is the association of a sub-millimetric bouncing drop moving along with a co-evolving Faraday wave. When confined in a harmonic potential, its stable trajectories are periodic and quantised both in extension and mean angular momentum. In this article, we present the rest of the story, specifically the chaotic paths. They are chaotic and show intermittent behaviors between an unstable quantised set of attractors. First, we present the two possible situations we find experimentally. Then, we emphasise theoretically two mechanisms that lead to unstable situations. It corresponds either to noise-driven chaos or low-dimensional deterministic chaos. Finally, we characterise experimentally each of these distinct situations. This article aims at presenting a comprehensive investigation of the unstable paths in order to complete the picture of walkers in a two dimensional harmonic potential.
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Affiliation(s)
- S Perrard
- Laboratoire FAST, CNRS UMR 7608, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - M Labousse
- Gulliver, CNRS UMR 7083, ESPCI Paris and PSL University, 75005 Paris, France
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33
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Delage R, Takayama Y, Biwa T. Bifurcation diagram of coupled thermoacoustic chaotic oscillators. CHAOS (WOODBURY, N.Y.) 2018; 28:083125. [PMID: 30180631 DOI: 10.1063/1.5037371] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Accepted: 07/24/2018] [Indexed: 06/08/2023]
Abstract
A thermoacoustic chaotic oscillator is a fluid system that presents thermally induced chaotic oscillations of a gas column. This study experimentally reports a bifurcation diagram when two thermoacoustic chaotic oscillators are dissipatively coupled to each other. The two-parameter bifurcation diagram is constructed by varying the frequency mismatch and the coupling strength. Complete chaos synchronization is observed in the region with a frequency mismatch of less than 1% of the uncoupled oscillator. In other regions, synchronization between quasiperiodic oscillations and that between limit-cycle oscillations and amplitude death are observed as well as asynchronous states.
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Affiliation(s)
- Rémi Delage
- Department of Mechanical Engineering, Tohoku University, Sendai 980-8579, Japan
| | - Yusuke Takayama
- Department of Mechanical Engineering, Tohoku University, Sendai 980-8579, Japan
| | - Tetsushi Biwa
- Department of Mechanical Engineering, Tohoku University, Sendai 980-8579, Japan
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34
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Denis-le Coarer F, Quirce A, Valle A, Pesquera L, Rodríguez MA, Panajotov K, Sciamanna M. Attractor hopping between polarization dynamical states in a vertical-cavity surface-emitting laser subject to parallel optical injection. Phys Rev E 2018; 97:032201. [PMID: 29776124 DOI: 10.1103/physreve.97.032201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Indexed: 06/08/2023]
Abstract
We present experimental and theoretical results of noise-induced attractor hopping between dynamical states found in a single transverse mode vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. These transitions involve dynamical states with different polarizations of the light emitted by the VCSEL. We report an experimental map identifying, in the injected power-frequency detuning plane, regions where attractor hopping between two, or even three, different states occur. The transition between these behaviors is characterized by using residence time distributions. We find multistability regions that are characterized by heavy-tailed residence time distributions. These distributions are characterized by a -1.83±0.17 power law. Between these regions we find coherence enhancement of noise-induced attractor hopping in which transitions between states occur regularly. Simulation results show that frequency detuning variations and spontaneous emission noise play a role in causing switching between attractors. We also find attractor hopping between chaotic states with different polarization properties. In this case, simulation results show that spontaneous emission noise inherent to the VCSEL is enough to induce this hopping.
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Affiliation(s)
- Florian Denis-le Coarer
- Instituto de Física de Cantabria, Consejo Superior de Investigaciones Científicas (CSIC), Universidad de Cantabria, 39005 Santander, Spain
- Chair in Photonics, LMOPS Laboratory, CentraleSupélec, Université de Paris-Saclay and Université de Lorraine, 57070 Metz, France
| | - Ana Quirce
- Vrije Universiteit Brussel, Faculty of Engineering Sciences, Brussels Photonics Team (B-PHOT), Pleinlaan 2, 1050 Brussels, Belgium
| | - Angel Valle
- Instituto de Física de Cantabria, Consejo Superior de Investigaciones Científicas (CSIC), Universidad de Cantabria, 39005 Santander, Spain
| | - Luis Pesquera
- Instituto de Física de Cantabria, Consejo Superior de Investigaciones Científicas (CSIC), Universidad de Cantabria, 39005 Santander, Spain
| | - Miguel A Rodríguez
- Instituto de Física de Cantabria, Consejo Superior de Investigaciones Científicas (CSIC), Universidad de Cantabria, 39005 Santander, Spain
| | - Krassimir Panajotov
- Vrije Universiteit Brussel, Faculty of Engineering Sciences, Brussels Photonics Team (B-PHOT), Pleinlaan 2, 1050 Brussels, Belgium
- Institute of Solid State Physics, 72 Tzarigradsko, Chaussee Blvd., 1784 Sofia, Bulgaria
| | - Marc Sciamanna
- Chair in Photonics, LMOPS Laboratory, CentraleSupélec, Université de Paris-Saclay and Université de Lorraine, 57070 Metz, France
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Choi D, Wishon MJ, Chang CY, Citrin DS, Locquet A. Multistate intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity. CHAOS (WOODBURY, N.Y.) 2018; 28:011102. [PMID: 29390638 DOI: 10.1063/1.5013332] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.
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Affiliation(s)
- Daeyoung Choi
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
| | - Michael J Wishon
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
| | - C Y Chang
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
| | - D S Citrin
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
| | - A Locquet
- Georgia Tech-CNRS UMI 2958, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz, France
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Duane GS, Grabow C, Selten F, Ghil M. Introduction to focus issue: Synchronization in large networks and continuous media-data, models, and supermodels. CHAOS (WOODBURY, N.Y.) 2017; 27:126601. [PMID: 29289046 DOI: 10.1063/1.5018728] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The synchronization of loosely coupled chaotic systems has increasingly found applications to large networks of differential equations and to models of continuous media. These applications are at the core of the present Focus Issue. Synchronization between a system and its model, based on limited observations, gives a new perspective on data assimilation. Synchronization among different models of the same system defines a supermodel that can achieve partial consensus among models that otherwise disagree in several respects. Finally, novel methods of time series analysis permit a better description of synchronization in a system that is only observed partially and for a relatively short time. This Focus Issue discusses synchronization in extended systems or in components thereof, with particular attention to data assimilation, supermodeling, and their applications to various areas, from climate modeling to macroeconomics.
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Affiliation(s)
- Gregory S Duane
- Geophysical Institute, University of Bergen, Postbox 7803, 5020 Bergen, Norway
| | | | - Frank Selten
- Royal Netherlands Meteorological Institute, De Bilt, The Netherlands
| | - Michael Ghil
- Geosciences Department, Ecole Normale Supérieure and PSL Resaerch University, Paris, France
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Delage R, Takayama Y, Biwa T. On-off intermittency in coupled chaotic thermoacoustic oscillations. CHAOS (WOODBURY, N.Y.) 2017; 27:043111. [PMID: 28456176 DOI: 10.1063/1.4981910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper documents on-off intermittency observed in coupled thermoacoustic chaotic oscillations. Mode competition between two or three oscillation modes engenders chaotic oscillations through quasiperiodic oscillations introduced by a local cross-sectional change in a gas-filled tube. Complete synchronization is then obtained by connecting two thermoacoustic chaotic oscillators via a rigid plate with an orifice. From the analysis of pressure fluctuations, theoretical statistical scaling laws related to the laminar phases, spectral density, and amplitude probability distribution are found to be satisfied in the coupled thermoacoustic oscillators, when the thermoacoustic complete synchronization breaks down through an on-off intermittency route with the decreased orifice size.
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Affiliation(s)
- Rémi Delage
- Department of Mechanical Engineering, Tohoku University, Sendai 980-8579, Japan
| | - Yusuke Takayama
- Department of Mechanical Engineering, Tohoku University, Sendai 980-8579, Japan
| | - Tetsushi Biwa
- Department of Mechanical Engineering, Tohoku University, Sendai 980-8579, Japan
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38
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Huang L, Ni X, Ditto WL, Spano M, Carney PR, Lai YC. Detecting and characterizing high-frequency oscillations in epilepsy: a case study of big data analysis. ROYAL SOCIETY OPEN SCIENCE 2017; 4:160741. [PMID: 28280577 PMCID: PMC5319343 DOI: 10.1098/rsos.160741] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2016] [Accepted: 12/22/2016] [Indexed: 05/08/2023]
Abstract
We develop a framework to uncover and analyse dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive datasets to eliminate erroneous data segments, application of the empirical mode decomposition and Hilbert transform paradigm to obtain the fundamental components embedded in the time series at distinct time scales, and statistical/scaling analysis of the components. As a case study, we apply our framework to detecting and characterizing high-frequency oscillations (HFOs) from a big database of rat electroencephalogram recordings. We find a striking phenomenon: HFOs exhibit on-off intermittency that can be quantified by algebraic scaling laws. Our framework can be generalized to big data-related problems in other fields such as large-scale sensor data and seismic data analysis.
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Affiliation(s)
- Liang Huang
- School of Physical Science and Technology, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
| | - Xuan Ni
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA
| | - William L. Ditto
- College of Sciences, North Carolina State University, Raleigh, NC 27695, USA
| | - Mark Spano
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ 85287, USA
| | - Paul R. Carney
- Pediatric Neurology and Epilepsy, Department of Neurology, University of North Carolina, 170 Manning Drive, Chapel Hill, NC 27599-7025, USA
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA
- Department of Physics, Arizona State University, Tempe, AZ 85287, USA
- Author for correspondence: Ying-Cheng Lai e-mail:
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39
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Medina JM, Díaz JA. Fluctuation scaling in the visual cortex at threshold. Phys Rev E 2016; 93:052403. [PMID: 27300920 DOI: 10.1103/physreve.93.052403] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2015] [Indexed: 11/07/2022]
Abstract
Fluctuation scaling relates trial-to-trial variability to the average response by a power function in many physical processes. Here we address whether fluctuation scaling holds in sensory psychophysics and its functional role in visual processing. We report experimental evidence of fluctuation scaling in human color vision and form perception at threshold. Subjects detected thresholds in a psychophysical masking experiment that is considered a standard reference for studying suppression between neurons in the visual cortex. For all subjects, the analysis of threshold variability that results from the masking task indicates that fluctuation scaling is a global property that modulates detection thresholds with a scaling exponent that departs from 2, β=2.48±0.07. We also examine a generalized version of fluctuation scaling between the sample kurtosis K and the sample skewness S of threshold distributions. We find that K and S are related and follow a unique quadratic form K=(1.19±0.04)S^{2}+(2.68±0.06) that departs from the expected 4/3 power function regime. A random multiplicative process with weak additive noise is proposed based on a Langevin-type equation. The multiplicative process provides a unifying description of fluctuation scaling and the quadratic S-K relation and is related to on-off intermittency in sensory perception. Our findings provide an insight into how the human visual system interacts with the external environment. The theoretical methods open perspectives for investigating fluctuation scaling and intermittency effects in a wide variety of natural, economic, and cognitive phenomena.
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Affiliation(s)
- José M Medina
- Departamento de Óptica, Facultad de Ciencias, Universidad de Granada, Edificio Mecenas, 18071, Granada, Spain
| | - José A Díaz
- Departamento de Óptica, Facultad de Ciencias, Universidad de Granada, Edificio Mecenas, 18071, Granada, Spain
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40
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Hramov AE, Koronovskii AA, Moskalenko OI, Zhuravlev MO, Jaimes-Reategui R, Pisarchik AN. Separation of coexisting dynamical regimes in multistate intermittency based on wavelet spectrum energies in an erbium-doped fiber laser. Phys Rev E 2016; 93:052218. [PMID: 27300891 DOI: 10.1103/physreve.93.052218] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2015] [Indexed: 06/06/2023]
Abstract
We propose a method for the detection and localization of different types of coexisting oscillatory regimes that alternate with each other leading to multistate intermittency. Our approach is based on consideration of wavelet spectrum energies. The proposed technique is tested in an erbium-doped fiber laser with four coexisting periodic orbits, where external noise induces intermittent switches between the coexisting states. Statistical characteristics of multistate intermittency, such as the mean duration of the phases for every oscillation type, are examined with the help of the developed method. We demonstrate strong advantages of the proposed technique over previously used amplitude methods.
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Affiliation(s)
- Alexander E Hramov
- Saratov State University, Astrakhanskaya, 83, Saratov 410012, Russia and Saratov State Technical University, Politehnicheskaya, 77, Saratov 410054, Russia
| | - Alexey A Koronovskii
- Saratov State University, Astrakhanskaya, 83, Saratov 410012, Russia and Saratov State Technical University, Politehnicheskaya, 77, Saratov 410054, Russia
| | - Olga I Moskalenko
- Saratov State University, Astrakhanskaya, 83, Saratov 410012, Russia and Saratov State Technical University, Politehnicheskaya, 77, Saratov 410054, Russia
| | - Maksim O Zhuravlev
- Saratov State University, Astrakhanskaya, 83, Saratov 410012, Russia and Saratov State Technical University, Politehnicheskaya, 77, Saratov 410054, Russia
| | - Rider Jaimes-Reategui
- Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, 47460, Lagos de Moreno, Jalisco, Mexico
| | - Alexander N Pisarchik
- Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcon, Madrid, Spain and Centro de Investigaciones en Optica, Loma del Bosque 115, Lomas del Campestre, 37150 Leon, Guanajuato, Mexico
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Koronovskii AA, Hramov AE, Grubov VV, Moskalenko OI, Sitnikova E, Pavlov AN. Coexistence of intermittencies in the neuronal network of the epileptic brain. Phys Rev E 2016; 93:032220. [PMID: 27078357 DOI: 10.1103/physreve.93.032220] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2015] [Indexed: 11/07/2022]
Abstract
Intermittent behavior occurs widely in nature. At present, several types of intermittencies are known and well-studied. However, consideration of intermittency has usually been limited to the analysis of cases when only one certain type of intermittency takes place. In this paper, we report on the temporal behavior of the complex neuronal network in the epileptic brain, when two types of intermittent behavior coexist and alternate with each other. We prove the presence of this phenomenon in physiological experiments with WAG/Rij rats being the model living system of absence epilepsy. In our paper, the deduced theoretical law for distributions of the lengths of laminar phases prescribing the power law with a degree of -2 agrees well with the experimental neurophysiological data.
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Affiliation(s)
- Alexey A Koronovskii
- Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.,Saratov State Technical University, Politehnicheskaja 77, Saratov 410056, Russia
| | - Alexander E Hramov
- Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.,Saratov State Technical University, Politehnicheskaja 77, Saratov 410056, Russia
| | - Vadim V Grubov
- Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.,Saratov State Technical University, Politehnicheskaja 77, Saratov 410056, Russia
| | - Olga I Moskalenko
- Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.,Saratov State Technical University, Politehnicheskaja 77, Saratov 410056, Russia
| | - Evgenia Sitnikova
- Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.,Institute of Higher Nervous Activity and Neurophysiology of Russian Academy of Science, Moscow, Russia
| | - Alexey N Pavlov
- Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.,Saratov State Technical University, Politehnicheskaja 77, Saratov 410056, Russia
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von Hardenberg J, Goluskin D, Provenzale A, Spiegel EA. Generation of Large-Scale Winds in Horizontally Anisotropic Convection. PHYSICAL REVIEW LETTERS 2015; 115:134501. [PMID: 26451558 DOI: 10.1103/physrevlett.115.134501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Indexed: 06/05/2023]
Abstract
We simulate three-dimensional, horizontally periodic Rayleigh-Bénard convection, confined between free-slip horizontal plates and rotating about a distant horizontal axis. When both the temperature difference between the plates and the rotation rate are sufficiently large, a strong horizontal wind is generated that is perpendicular to both the rotation vector and the gravity vector. The wind is turbulent, large-scale, and vertically sheared. Horizontal anisotropy, engendered here by rotation, appears necessary for such wind generation. Most of the kinetic energy of the flow resides in the wind, and the vertical turbulent heat flux is much lower on average than when there is no wind.
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Affiliation(s)
- J von Hardenberg
- Institute of Atmospheric Sciences, National Research Council, Torino 10133, Italy
| | - D Goluskin
- Mathematics Department, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor 48109, Michigan, USA
| | - A Provenzale
- Institute of Geosciences and Earth Resources, National Research Council, Pisa 56124, Italy
| | - E A Spiegel
- Astronomy Department, Columbia University, New York, New York 10027, USA
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43
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Campos-Mejía A, Pisarchik AN, Sevilla-Escoboza R, Huerta-Cuellar G, Vera-Ávila VP. Coherence enhanced intermittency in an optically injected semiconductor laser. OPTICS EXPRESS 2015; 23:10428-10434. [PMID: 25969084 DOI: 10.1364/oe.23.010428] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We report on the experimental observation of coherence enhancement of noise-induced intermittency in a semiconductor laser subject to optical injection from another laser at the boundary of the frequency-locking regime. The intermittent switches between locked and unlocked states occur more regularly at a certain value of the injecting laser pump current. A shape of probability distribution of the experimental inter-spike-interval fluctuations is used to quantitatively characterize the intermittent behavior.
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45
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Harrison HS, Kelty-Stephen DG, Vaz DV, Michaels CF. Multiplicative-cascade dynamics in pole balancing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:060903. [PMID: 25019712 DOI: 10.1103/physreve.89.060903] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2014] [Indexed: 06/03/2023]
Abstract
Pole balancing is a key task for probing the prospective control that organisms must engage in for purposeful action. The temporal structure of pole-balancing behaviors will reflect the on-line operation of control mechanisms needed to maintain an upright posture. In this study, signatures of multifractality are sought and found in time series of the vertical angle of a pole balanced on the fingertip. Comparisons to surrogate time series reveal multiplicative-cascade dynamics and interactivity across scales. In addition, simulations of a pole-balancing model generating on-off intermittency [J. L. Cabrera and J. G. Milton, Phys. Rev. Lett. 89, 158702 (2002)] were analyzed. Evidence of multifractality is also evident in simulations, though comparing simulated and participant series reveals a significantly greater contribution of cross-scale interactivity for the latter. These findings suggest that multiplicative-cascade dynamics are an extension of on-off intermittency and play a role in prospective coordination.
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Affiliation(s)
- Henry S Harrison
- Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Unit 1020, Storrs, Connecticut 06269-1020, USA
| | - Damian G Kelty-Stephen
- Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Unit 1020, Storrs, Connecticut 06269-1020, USA and Department of Psychology, Grinnell College, 1116 8th Avenue, Grinnell, Iowa 50112, USA
| | - Daniela V Vaz
- Department of Physical Therapy, Universidade Federal de Minas Gerais, Avenida Presidente Antônio Carlos, 6627, Belo Horizonte, MG, 31270-901, Brazil
| | - Claire F Michaels
- Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Unit 1020, Storrs, Connecticut 06269-1020, USA
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46
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Hicke K, Porte X, Fischer I. Characterizing the deterministic nature of individual power dropouts in semiconductor lasers subject to delayed feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052904. [PMID: 24329328 DOI: 10.1103/physreve.88.052904] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2013] [Revised: 10/07/2013] [Indexed: 06/03/2023]
Abstract
We implement a method to identify the deterministic nature of specific events in the dynamics of a semiconductor laser subject to time-delayed optical feedback. Specifically, we study the power dropouts in the low-frequency fluctuations regime on an individual event basis and identify whether the underlying dominant mechanism is deterministic. Our approach is based on sychronization with a twin system in a symmetric relay configuration. We investigate the dependence of the fraction of deterministically driven (i.e., synchronized) dropouts on the laser's pump current as a key parameter. Our experimental results are corroborated by numerical modeling based on rate equations. Our numerical findings also provide insights into the influence of spontaneous emission noise.
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Affiliation(s)
- K Hicke
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - X Porte
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - I Fischer
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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Hramov AE, Koronovskii AA, Moskalenko OI, Zhuravlev MO, Ponomarenko VI, Prokhorov MD. Intermittency of intermittencies. CHAOS (WOODBURY, N.Y.) 2013; 23:033129. [PMID: 24089965 DOI: 10.1063/1.4819899] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
A phenomenon of intermittency of intermittencies is discovered in the temporal behavior of two coupled complex systems. We observe for the first time the coexistence of two types of intermittent behavior taking place simultaneously near the boundary of the synchronization regime of coupled chaotic oscillators. This phenomenon is found both in the numerical and physiological experiments. The laws for both the distribution and mean length of laminar phases versus the control parameter values are analytically deduced. A very good agreement between the theoretical results and simulation is shown.
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48
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Different types of synchrony in chaotic and cyclic communities. Nat Commun 2013; 4:1359. [PMID: 23322047 DOI: 10.1038/ncomms2355] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2012] [Accepted: 12/03/2012] [Indexed: 11/08/2022] Open
Abstract
Stability and persistence of populations is of great interest for management and conservation purposes. Spatial dynamics can have a crucial role in population stability via synchronization, and beneficial and detrimental effects on population persistence have been shown. Despite a theoretical understanding of synchronization, empirical data on synchrony of populations are restricted to systems that do not display the full spectrum of complex dynamics that may occur in nature (that is, chaos or quasiperiodicity). Here we show in experiments that the qualitative form of dynamic behaviour of chaotic and periodic oscillating communities did not change when unidirectionally coupled to oscillating driver communities. Driver and response populations were phase locked in cyclic communities, whereas chaotic communities showed only short periods of statistical coherencies. Our study provides the first empirical analysis of synchronization of chaotic communities and shows that the likelihood for chaos is not lowered in spatially explicit systems but that cyclic and chaotic systems differ in synchronization.
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49
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Ruseckas J, Kaulakys B. Intermittency in relation with 1/f noise and stochastic differential equations. CHAOS (WOODBURY, N.Y.) 2013; 23:023102. [PMID: 23822467 DOI: 10.1063/1.4802429] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
One of the models of intermittency is on-off intermittency, arising due to time-dependent forcing of a bifurcation parameter through a bifurcation point. For on-off intermittency, the power spectral density (PSD) of the time-dependent deviation from the invariant subspace in a low frequency region exhibits 1/√f power-law noise. Here, we investigate a mechanism of intermittency, similar to the on-off intermittency, occurring in nonlinear dynamical systems with invariant subspace. In contrast to the on-off intermittency, we consider the case where the transverse Lyapunov exponent is zero. We show that for such nonlinear dynamical systems, the power spectral density of the deviation from the invariant subspace can have 1/f(β) form in a wide range of frequencies. That is, such nonlinear systems exhibit 1/f noise. The connection with the stochastic differential equations generating 1/f(β) noise is established and analyzed, as well.
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Affiliation(s)
- J Ruseckas
- Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania.
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50
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Zhang F, Chen G, Li C, Kurths J. Chaos synchronization in fractional differential systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2013; 371:20120155. [PMID: 23547232 DOI: 10.1098/rsta.2012.0155] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
This paper presents a brief overview of recent developments in chaos synchronization in coupled fractional differential systems, where the original viewpoints are retained. In addition to complete synchronization, several other extended concepts of synchronization, such as projective synchronization, hybrid projective synchronization, function projective synchronization, generalized synchronization and generalized projective synchronization in fractional differential systems, are reviewed.
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Affiliation(s)
- Fengrong Zhang
- College of Science, China University of Petroleum (East China), Qingdao 266555, People's Republic of China
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