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Joo P, Kim M, Kish B, Nair VV, Tong Y, Liu Z, O'Brien ARW, Harte SE, Harris RE, Lee U, Wang Y. Brain network hypersensitivity underlies pain crises in sickle cell disease. Sci Rep 2024; 14:7315. [PMID: 38538687 PMCID: PMC10973361 DOI: 10.1038/s41598-024-57473-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2023] [Accepted: 03/18/2024] [Indexed: 04/04/2024] Open
Abstract
Sickle cell disease (SCD) is a genetic disorder causing painful and unpredictable Vaso-occlusive crises (VOCs) through blood vessel blockages. In this study, we propose explosive synchronization (ES) as a novel approach to comprehend the hypersensitivity and occurrence of VOCs in the SCD brain network. We hypothesized that the accumulated disruptions in the brain network induced by SCD might lead to strengthened ES and hypersensitivity. We explored ES's relationship with patient reported outcome measures (PROMs) as well as VOCs by analyzing EEG data from 25 SCD patients and 18 matched controls. SCD patients exhibited lower alpha frequency than controls. SCD patients showed correlation between frequency disassortativity (FDA), an ES condition, and three important PROMs. Furthermore, stronger FDA was observed in SCD patients with a higher frequency of VOCs and EEG recording near VOC. We also conducted computational modeling on SCD brain network to study FDA's role in network sensitivity. Our model demonstrated that a stronger FDA could be linked to increased sensitivity and frequency of VOCs. This study establishes connections between SCD pain and the universal network mechanism, ES, offering a strong theoretical foundation. This understanding will aid predicting VOCs and refining pain management for SCD patients.
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Affiliation(s)
- Pangyu Joo
- Department of Anesthesiology, Center for Consciousness Science, Center for the Study of Complex Systems, Michigan Psychedelic Center, University of Michigan, Arbor Lakes Building 1 Suite 2200, 4251 Plymouth Road, Ann Arbor, MI, 48105, USA
| | - Minkyung Kim
- Department of Anesthesiology, Center for Consciousness Science, Center for the Study of Complex Systems, Michigan Psychedelic Center, University of Michigan, Arbor Lakes Building 1 Suite 2200, 4251 Plymouth Road, Ann Arbor, MI, 48105, USA
| | - Brianna Kish
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA
| | | | - Yunjie Tong
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA
| | - Ziyue Liu
- Indiana Center for Musculoskeletal Health, Indiana University, Indianapolis, IN, USA
- Department of Biostatistics, Indiana University School of Medicine, Indianapolis, IN, USA
| | - Andrew R W O'Brien
- Division of Hematology/Oncology, Department of Medicine, Indiana University School of Medicine, Indianapolis, IN, USA
| | - Steven E Harte
- Department of Anesthesiology, Chronic Pain and Fatigue Research Center, University of Michigan, Ann Arbor, MI, USA
| | - Richard E Harris
- Department of Anesthesiology, Chronic Pain and Fatigue Research Center, University of Michigan, Ann Arbor, MI, USA
- Susan Samueli Integrative Health Institute, and Department of Anesthesiology and Perioperative Care, School of Medicine, University of California at Irvine, Irvine, CA, USA
| | - UnCheol Lee
- Department of Anesthesiology, Center for Consciousness Science, Center for the Study of Complex Systems, Michigan Psychedelic Center, University of Michigan, Arbor Lakes Building 1 Suite 2200, 4251 Plymouth Road, Ann Arbor, MI, 48105, USA.
| | - Ying Wang
- Division of Hematology/Oncology, Department of Medicine, Indiana University School of Medicine, Indianapolis, IN, USA.
- Department of Anesthesia, Stark Neurosciences Research Institute, Indiana University School of Medicine, Stark Neuroscience Building, Rm# 514E, 320 West 15th Street, Indianapolis, IN, 46202, USA.
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Joo P, Kim M, Kish B, Nair VV, Tong Y, Harte SE, Harris RE, Lee U, Wang Y. Brain network hypersensitivity underlies pain crises in sickle cell disease. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2023:2023.10.08.23296715. [PMID: 37873459 PMCID: PMC10593022 DOI: 10.1101/2023.10.08.23296715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2023]
Abstract
Sickle cell disease (SCD) is a genetic disorder causing blood vessel blockages and painful Vaso-occlusive crises (VOCs). VOCs, characterized by severe pain due to blocked blood flow, are recurrent and unpredictable, posing challenges for preventive strategies. In this study we propose explosive synchronization (ES), a phenomenon characterized by abrupt brain network phase transitions, as a novel approach to address this challenge. We hypothesized that the accumulated disruptions in the brain network induced by SCD might lead to strengthened ES and hypersensitivity. We explored ES's relationship with patient reported outcome measures (PROMs) and VOCs by analyzing EEG data from 25 SCD patients and 18 matched controls. SCD patients exhibited significantly lower alpha wave frequency than controls. SCD patients under painful pressure stimulation showed correlation between frequency disassortativity (FDA), an ES condition, and three important PROMs. Furthermore, patients who had a higher frequency of VOCs in the preceding 12 months presented with stronger FDA. The timing of VOC occurrence relative to EEG recordings was significantly associated to FDA. We also conducted computational modeling on SCD brain network to study FDA's role in network sensitivity. Stronger FDA correlated with higher responsivity and complexity in our model. Simulation under noisy environment showed that higher FDA could be linked to increased occurrence frequency of crisis. This study establishes connections between SCD pain and the universal network mechanism, ES, offering a strong theoretical foundation. This understanding will aid predicting VOCs and refining pain management for SCD patients.
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Srinivasan K, Coble N, Hamlin J, Antonsen T, Ott E, Girvan M. Parallel Machine Learning for Forecasting the Dynamics of Complex Networks. PHYSICAL REVIEW LETTERS 2022; 128:164101. [PMID: 35522516 DOI: 10.1103/physrevlett.128.164101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 03/28/2022] [Indexed: 06/14/2023]
Abstract
Forecasting the dynamics of large, complex, sparse networks from previous time series data is important in a wide range of contexts. Here we present a machine learning scheme for this task using a parallel architecture that mimics the topology of the network of interest. We demonstrate the utility and scalability of our method implemented using reservoir computing on a chaotic network of oscillators. Two levels of prior knowledge are considered: (i) the network links are known, and (ii) the network links are unknown and inferred via a data-driven approach to approximately optimize prediction.
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Affiliation(s)
| | - Nolan Coble
- University of Maryland, College Park, Maryland 20742, USA
- SUNY Brockport, Brockport, New York 14420, USA
| | - Joy Hamlin
- Stony Brook University, Long Island, New York 11794, USA
| | | | - Edward Ott
- University of Maryland, College Park, Maryland 20742, USA
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Laing CR, Bläsche C, Means S. Dynamics of Structured Networks of Winfree Oscillators. Front Syst Neurosci 2021; 15:631377. [PMID: 33643004 PMCID: PMC7902706 DOI: 10.3389/fnsys.2021.631377] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Accepted: 01/18/2021] [Indexed: 01/01/2023] Open
Abstract
Winfree oscillators are phase oscillator models of neurons, characterized by their phase response curve and pulsatile interaction function. We use the Ott/Antonsen ansatz to study large heterogeneous networks of Winfree oscillators, deriving low-dimensional differential equations which describe the evolution of the expected state of networks of oscillators. We consider the effects of correlations between an oscillator's in-degree and out-degree, and between the in- and out-degrees of an “upstream” and a “downstream” oscillator (degree assortativity). We also consider correlated heterogeneity, where some property of an oscillator is correlated with a structural property such as degree. We finally consider networks with parameter assortativity, coupling oscillators according to their intrinsic frequencies. The results show how different types of network structure influence its overall dynamics.
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Affiliation(s)
- Carlo R Laing
- School of Natural and Computational Sciences, Massey University, Auckland, New Zealand
| | - Christian Bläsche
- School of Natural and Computational Sciences, Massey University, Auckland, New Zealand
| | - Shawn Means
- School of Natural and Computational Sciences, Massey University, Auckland, New Zealand
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Brister BN, Belykh VN, Belykh IV. When three is a crowd: Chaos from clusters of Kuramoto oscillators with inertia. Phys Rev E 2020; 101:062206. [PMID: 32688588 DOI: 10.1103/physreve.101.062206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2020] [Accepted: 06/01/2020] [Indexed: 06/11/2023]
Abstract
Modeling cooperative dynamics using networks of phase oscillators is common practice for a wide spectrum of biological and technological networks, ranging from neuronal populations to power grids. In this paper we study the emergence of stable clusters of synchrony with complex intercluster dynamics in a three-population network of identical Kuramoto oscillators with inertia. The populations have different sizes and can split into clusters where the oscillators synchronize within a cluster, but notably, there is a phase shift between the dynamics of the clusters. We extend our previous results on the bistability of synchronized clusters in a two-population network [I. V. Belykh et al., Chaos 26, 094822 (2016)CHAOEH1054-150010.1063/1.4961435] and demonstrate that the addition of a third population can induce chaotic intercluster dynamics. This effect can be captured by the old adage "two is company, three is a crowd," which suggests that the delicate dynamics of a romantic relationship may be destabilized by the addition of a third party, leading to chaos. Through rigorous analysis and numerics, we demonstrate that the intercluster phase shifts can stably coexist and exhibit different forms of chaotic behavior, including oscillatory, rotatory, and mixed-mode oscillations. We also discuss the implications of our stability results for predicting the emergence of chimeras and solitary states.
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Affiliation(s)
- Barrett N Brister
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA
| | - Vladimir N Belykh
- Department of Mathematics, Volga State University of Water Transport, 5A Nesterov street, Nizhny Novgorod 603950, Russia
- Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia
| | - Igor V Belykh
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA
- Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia
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Skardal PS. Low-dimensional dynamics of the Kuramoto model with rational frequency distributions. Phys Rev E 2018; 98:022207. [PMID: 30253541 DOI: 10.1103/physreve.98.022207] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Indexed: 11/07/2022]
Abstract
The Kuramoto model is a paradigmatic tool for studying the dynamics of collective behavior in large ensembles of coupled dynamical systems. Over the past decade a great deal of progress has been made in analytical descriptions of the macroscopic dynamics of the Kuramoto model, facilitated by the discovery of Ott and Antonsen's dimensionality reduction method. However, the vast majority of these works relies on a critical assumption where the oscillators' natural frequencies are drawn from a Cauchy, or Lorentzian, distribution, which allows for a convenient closure of the evolution equations from the dimensionality reduction. In this paper we investigate the low-dimensional dynamics that emerge from a broader family of natural frequency distributions, in particular, a family of rational distribution functions. We show that, as the polynomials that characterize the frequency distribution increase in order, the low-dimensional evolution equations become more complicated, but nonetheless the system dynamics remain simple, displaying a transition from incoherence to partial synchronization at a critical coupling strength. Using the low-dimensional equations we analytically calculate the critical coupling strength corresponding to the onset of synchronization and investigate the scaling properties of the order parameter near the onset of synchronization. These results agree with calculations from Kuramoto's original self-consistency framework, but we emphasize that the low-dimensional equations approach used here allows for a true stability analysis categorizing the bifurcations.
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Wieland S, Malerba SB, Aumaitre S, Bercegol H. Mean-field approach for frequency synchronization in complex networks of two oscillator types. Phys Rev E 2018; 97:052310. [PMID: 29906922 DOI: 10.1103/physreve.97.052310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2017] [Indexed: 06/08/2023]
Abstract
Oscillator networks with an asymmetric bipolar distribution of natural frequencies are useful representations of power grids. We propose a mean-field model that captures the onset, form, and linear stability of frequency synchronization in such oscillator networks. The model takes into account a broad class of heterogeneous connection structures and identifies a functional form as well as basic properties that synchronized regimes possess classwide. The framework also captures synchronized regimes with large phase differences that commonly appear just above the critical threshold. Additionally, the accuracy of mean-field assumptions can be gauged internally through two model quantities. With our framework, the impact of local grid structure on frequency synchronization can be systematically explored.
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Affiliation(s)
- Stefan Wieland
- SPEC, CEA, CNRS UMR 3680, Université Paris-Saclay, F-91191 Gif-sur-Yvette Cedex, France
| | - Simone Blanco Malerba
- SPEC, CEA, CNRS UMR 3680, Université Paris-Saclay, F-91191 Gif-sur-Yvette Cedex, France
| | - Sébastien Aumaitre
- SPEC, CEA, CNRS UMR 3680, Université Paris-Saclay, F-91191 Gif-sur-Yvette Cedex, France
| | - Hervé Bercegol
- SPEC, CEA, CNRS UMR 3680, Université Paris-Saclay, F-91191 Gif-sur-Yvette Cedex, France
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Skardal PS, Restrepo JG, Ott E. Uncovering low dimensional macroscopic chaotic dynamics of large finite size complex systems. CHAOS (WOODBURY, N.Y.) 2017; 27:083121. [PMID: 28863484 DOI: 10.1063/1.4986957] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
In the last decade, it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the macroscopic dynamics of other similar systems also have a low dimensional description in the infinite N limit has, however, remained elusive. In this paper, we show how techniques originally designed to analyze noisy experimental chaotic time series can be used to identify effective low dimensional macroscopic descriptions from simulations with a finite number of elements. We illustrate and verify the effectiveness of our approach by applying it to the dynamics of an ensemble of globally coupled Landau-Stuart oscillators for which we demonstrate low dimensional macroscopic chaotic behavior with an effective 4-dimensional description. By using this description, we show that one can calculate dynamical invariants such as Lyapunov exponents and attractor dimensions. One could also use the reconstruction to generate short-term predictions of the macroscopic dynamics.
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Affiliation(s)
| | - Juan G Restrepo
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
| | - Edward Ott
- Department of Physics and Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA
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Chandra S, Hathcock D, Crain K, Antonsen TM, Girvan M, Ott E. Modeling the network dynamics of pulse-coupled neurons. CHAOS (WOODBURY, N.Y.) 2017; 27:033102. [PMID: 28364765 DOI: 10.1063/1.4977514] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network. This dimensional reduction allows for an efficient characterization of system phase transitions and attractors. For networks with tightly peaked degree distributions, the macroscopic behavior closely resembles that of fully connected networks previously studied by others. In contrast, networks with highly skewed degree distributions exhibit different macroscopic dynamics due to the emergence of degree dependent behavior of different oscillators. For nonassortative networks (i.e., networks without degree correlations), we observe the presence of a synchronously firing phase that can be suppressed by the presence of either assortativity or disassortativity in the network. We show that the results derived here can be used to analyze the effects of network topology on macroscopic behavior in neuronal networks in a computationally efficient fashion.
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Affiliation(s)
| | - David Hathcock
- Case Western Reserve University, Cleveland, Ohio 44016, USA
| | | | | | | | - Edward Ott
- University of Maryland, College Park, Maryland 20742, USA
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Pietras B, Daffertshofer A. Ott-Antonsen attractiveness for parameter-dependent oscillatory systems. CHAOS (WOODBURY, N.Y.) 2016; 26:103101. [PMID: 27802676 DOI: 10.1063/1.4963371] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
The Ott-Antonsen (OA) ansatz [Ott and Antonsen, Chaos 18, 037113 (2008); Chaos 19, 023117 (2009)] has been widely used to describe large systems of coupled phase oscillators. If the coupling is sinusoidal and if the phase dynamics does not depend on the specific oscillator, then the macroscopic behavior of the systems can be fully described by a low-dimensional dynamics. Does the corresponding manifold remain attractive when introducing an intrinsic dependence between an oscillator's phase and its dynamics by additional, oscillator specific parameters? To answer this, we extended the OA ansatz and proved that parameter-dependent oscillatory systems converge to the OA manifold given certain conditions. Our proof confirms recent numerical findings that already hinted at this convergence. Furthermore, we offer a thorough mathematical underpinning for networks of so-called theta neurons, where the OA ansatz has just been applied. In a final step, we extend our proof by allowing for time-dependent and multi-dimensional parameters as well as for network topologies other than global coupling. This renders the OA ansatz an excellent starting point for the analysis of a broad class of realistic settings.
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Affiliation(s)
- Bastian Pietras
- Faculty of Behavioural and Movement Sciences, MOVE Research Institute Amsterdam and Institute for Brain and Behavior Amsterdam, Vrije Universiteit Amsterdam, van der Boechorststraat 9, Amsterdam 1081 BT, The Netherlands
| | - Andreas Daffertshofer
- Faculty of Behavioural and Movement Sciences, MOVE Research Institute Amsterdam and Institute for Brain and Behavior Amsterdam, Vrije Universiteit Amsterdam, van der Boechorststraat 9, Amsterdam 1081 BT, The Netherlands
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Skardal PS, Taylor D, Sun J. Optimal synchronization of directed complex networks. CHAOS (WOODBURY, N.Y.) 2016; 26:094807. [PMID: 27781463 PMCID: PMC4920812 DOI: 10.1063/1.4954221] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2016] [Accepted: 05/16/2016] [Indexed: 05/29/2023]
Abstract
We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized synchrony alignment function that encodes the interplay between the network structure and the oscillators' natural frequencies and serves as an objective measure for the network's degree of synchronization. Using the generalized synchrony alignment function, we show that a network's synchronization properties can be systematically optimized. This framework also allows us to study the properties of synchrony-optimized networks, and in particular, investigate the role of directed network properties such as nodal in- and out-degrees. For instance, we find that in optimally rewired networks, the heterogeneity of the in-degree distribution roughly matches the heterogeneity of the natural frequency distribution, but no such relationship emerges for out-degrees. We also observe that a network's synchronization properties are promoted by a strong correlation between the nodal in-degrees and the natural frequencies of oscillators, whereas the relationship between the nodal out-degrees and the natural frequencies has comparatively little effect. This result is supported by our theory, which indicates that synchronization is promoted by a strong alignment of the natural frequencies with the left singular vectors corresponding to the largest singular values of the Laplacian matrix.
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Affiliation(s)
| | - Dane Taylor
- Department of Mathematics, Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| | - Jie Sun
- Department of Mathematics, Clarkson University, Potsdam, New York 13699, USA
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12
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Skardal PS, Arenas A. On controlling networks of limit-cycle oscillators. CHAOS (WOODBURY, N.Y.) 2016; 26:094812. [PMID: 27781472 DOI: 10.1063/1.4954273] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here, we study the control of network-coupled limit cycle oscillators, extending the previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of controls. The first type directs oscillators towards larger amplitudes, while the second does not. We present numerical examples of both control types and comment on the potential failures of the method.
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Affiliation(s)
| | - Alex Arenas
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain
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13
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Skardal PS, Taylor D, Sun J, Arenas A. Erosion of synchronization: Coupling heterogeneity and network structure. PHYSICA D. NONLINEAR PHENOMENA 2016; 323-324:40-48. [PMID: 27909350 PMCID: PMC5125783 DOI: 10.1016/j.physd.2015.10.015] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We study the dynamics of network-coupled phase oscillators in the presence of coupling frustration. It was recently demonstrated that in heterogeneous network topologies, the presence of coupling frustration causes perfect phase synchronization to become unattainable even in the limit of infinite coupling strength. Here, we consider the important case of heterogeneous coupling functions and extend previous results by deriving analytical predictions for the total erosion of synchronization. Our analytical results are given in terms of basic quantities related to the network structure and coupling frustration. In addition to fully heterogeneous coupling, where each individual interaction is allowed to be distinct, we also consider partially heterogeneous coupling and homogeneous coupling in which the coupling functions are either unique to each oscillator or identical for all network interactions, respectively. We demonstrate the validity of our theory with numerical simulations of multiple network models, and highlight the interesting effects that various coupling choices and network models have on the total erosion of synchronization. Finally, we consider some special network structures with well-known spectral properties, which allows us to derive further analytical results.
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Affiliation(s)
- Per Sebastian Skardal
- Department of Mathematics, Trinity College, Hartford, CT 06106, USA
- Departament d’Enginyeria Informatica i Matemátiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - Dane Taylor
- Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA
| | - Jie Sun
- Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA
| | - Alex Arenas
- Departament d’Enginyeria Informatica i Matemátiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
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14
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Hong H, O'Keeffe KP, Strogatz SH. Phase coherence induced by correlated disorder. Phys Rev E 2016; 93:022219. [PMID: 26986343 DOI: 10.1103/physreve.93.022219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2016] [Indexed: 06/05/2023]
Abstract
We consider a mean-field model of coupled phase oscillators with quenched disorder in the coupling strengths and natural frequencies. When these two kinds of disorder are uncorrelated (and when the positive and negative couplings are equal in number and strength), it is known that phase coherence cannot occur and synchronization is absent. Here we explore the effects of correlating the disorder. Specifically, we assume that any given oscillator either attracts or repels all the others, and that the sign of the interaction is deterministically correlated with the given oscillator's natural frequency. For symmetrically correlated disorder with zero mean, we find that the system spontaneously synchronizes, once the width of the frequency distribution falls below a critical value. For asymmetrically correlated disorder, the model displays coherent traveling waves: the complex order parameter becomes nonzero and rotates with constant frequency different from the system's mean natural frequency. Thus, in both cases, correlated disorder can trigger phase coherence.
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Affiliation(s)
- Hyunsuk Hong
- Department of Physics and Research Institute of Physics and Chemistry, Chonbuk National University, Jeonju 561-756, Korea
| | - Kevin P O'Keeffe
- Center for Applied Mathematics, Cornell University, New York 14853, USA
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