1
|
Mirasso CR, Carelli PV, Pereira T, Matias FS, Copelli M. Anticipated and zero-lag synchronization in motifs of delay-coupled systems. CHAOS (WOODBURY, N.Y.) 2017; 27:114305. [PMID: 29195321 DOI: 10.1063/1.5006932] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Anticipated and zero-lag synchronization have been observed in different scientific fields. In the brain, they might play a fundamental role in information processing, temporal coding and spatial attention. Recent numerical work on anticipated and zero-lag synchronization studied the role of delays. However, an analytical understanding of the conditions for these phenomena remains elusive. In this paper, we study both phenomena in systems with small delays. By performing a phase reduction and studying phase locked solutions, we uncover the functional relation between the delay, excitation and inhibition for the onset of anticipated synchronization in a sender-receiver-interneuron motif. In the case of zero-lag synchronization in a chain motif, we determine the stability conditions. These analytical solutions provide an excellent prediction of the phase-locked regimes of Hodgkin-Huxley models and Roessler oscillators.
Collapse
Affiliation(s)
- Claudio R Mirasso
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Universitat de les Illes Baleares, Campus UIB, E-07122 Palma de Mallorca, Spain
| | - Pedro V Carelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil
| | - Tiago Pereira
- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, São Paulo, Brazil
| | - Fernanda S Matias
- Departamento de Física, Universidade Federal de Alagoas, Maceió, Alagoas, Brazil
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil
| |
Collapse
|
2
|
Segall K, LeGro M, Kaplan S, Svitelskiy O, Khadka S, Crotty P, Schult D. Synchronization dynamics on the picosecond time scale in coupled Josephson junction neurons. Phys Rev E 2017; 95:032220. [PMID: 28415246 DOI: 10.1103/physreve.95.032220] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Indexed: 11/07/2022]
Abstract
Conventional digital computation is rapidly approaching physical limits for speed and energy dissipation. Here we fabricate and test a simple neuromorphic circuit that models neuronal somas, axons, and synapses with superconducting Josephson junctions. The circuit models two mutually coupled excitatory neurons. In some regions of parameter space the neurons are desynchronized. In others, the Josephson neurons synchronize in one of two states, in-phase or antiphase. An experimental alteration of the delay and strength of the connecting synapses can toggle the system back and forth in a phase-flip bifurcation. Firing synchronization states are calculated >70 000 times faster than conventional digital approaches. With their speed and low energy dissipation (10^{-17}J/spike), this set of proof-of-concept experiments establishes Josephson junction neurons as a viable approach for improvements in neuronal computation as well as applications in neuromorphic computing.
Collapse
Affiliation(s)
- K Segall
- Department of Physics and Astronomy, Colgate University, 13 Oak Drive, Hamilton, New York 13346, USA
| | - M LeGro
- Department of Physics and Astronomy, Colgate University, 13 Oak Drive, Hamilton, New York 13346, USA
| | - S Kaplan
- Consultant, 1800 Cherokee Drive, Estes Park, Colorado 80517, USA
| | - O Svitelskiy
- Department of Physics and Astronomy, Colgate University, 13 Oak Drive, Hamilton, New York 13346, USA
| | - S Khadka
- Department of Physics and Astronomy, Colgate University, 13 Oak Drive, Hamilton, New York 13346, USA
| | - P Crotty
- Department of Physics and Astronomy, Colgate University, 13 Oak Drive, Hamilton, New York 13346, USA
| | - D Schult
- Department of Mathematics, Colgate University, 13 Oak Drive, Hamilton, New York 13346, USA
| |
Collapse
|
3
|
McKetterick TJ, Giuggioli L. Exact dynamics of stochastic linear delayed systems: application to spatiotemporal coordination of comoving agents. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042135. [PMID: 25375466 DOI: 10.1103/physreve.90.042135] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Indexed: 06/04/2023]
Abstract
Delayed dynamics result from finite transmission speeds of a signal in the form of energy, mass, or information. In stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic, oscillatory, and unstable evolution. Despite the vast literature, quantifying this rich behavior is limited by a lack of explicit analytic studies of high-dimensional stochastic delay systems. Here we fill this gap for systems governed by a linear Langevin equation of any number of delays and spatial dimensions with additive Gaussian noise. By exploiting Laplace transforms we are able to derive an exact time-dependent analytic solution of the Langevin equation. By using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables. As an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment. We propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay. We highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and/or in their spatial separation. We also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay.
Collapse
Affiliation(s)
- Thomas John McKetterick
- Bristol Centre for Complexity Sciences, University of Bristol, Bristol BS8 1UG, United Kingdom and Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UG, Kingdom
| | - Luca Giuggioli
- Bristol Centre for Complexity Sciences, University of Bristol, Bristol BS8 1UG, United Kingdom and Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UG, Kingdom and School of Biological Sciences, University of Bristol, Bristol BS8 1UG, United Kingdom
| |
Collapse
|
4
|
Szalai R, Orosz G. Decomposing the dynamics of heterogeneous delayed networks with applications to connected vehicle systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:040902. [PMID: 24229105 DOI: 10.1103/physreve.88.040902] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2013] [Indexed: 06/02/2023]
Abstract
Delay-coupled networks are investigated with nonidentical delay times and the effects of such heterogeneity on the emergent dynamics of complex systems are characterized. A simple decomposition method is presented that decouples the dynamics of the network into node-size modal equations in the vicinity of equilibria. The resulting independent components contain distributed delays that map the spatiotemporal complexity of the system to the time domain. We demonstrate that this approach can be used to reveal physical phenomena in heterogenous vehicular traffic when vehicles are linked via vehicle-to-vehicle communication.
Collapse
Affiliation(s)
- Róbert Szalai
- Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, United Kingdom
| | | |
Collapse
|
5
|
Kyrychko YN, Blyuss KB, Schöll E. Amplitude and phase dynamics in oscillators with distributed-delay coupling. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2013; 371:20120466. [PMID: 23960224 DOI: 10.1098/rsta.2012.0466] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
This paper studies the effects of distributed-delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, the conditions for amplitude death are obtained in terms of average frequency, frequency detuning and the parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insights into the dynamics inside amplitude death regions, the eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated, using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions.
Collapse
Affiliation(s)
- Y N Kyrychko
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK.
| | | | | |
Collapse
|
6
|
Wall E, Guichard F, Humphries AR. Synchronization in ecological systems by weak dispersal coupling with time delay. THEOR ECOL-NETH 2013. [DOI: 10.1007/s12080-013-0176-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
7
|
Abstract
Modern imaging methods allow a non-invasive assessment of both structural and functional brain connectivity. This has lead to the identification of disease-related alterations affecting functional connectivity. The mechanism of how such alterations in functional connectivity arise in a structured network of interacting neural populations is as yet poorly understood. Here we use a modeling approach to explore the way in which this can arise and to highlight the important role that local population dynamics can have in shaping emergent spatial functional connectivity patterns. The local dynamics for a neural population is taken to be of the Wilson–Cowan type, whilst the structural connectivity patterns used, describing long-range anatomical connections, cover both realistic scenarios (from the CoComac database) and idealized ones that allow for more detailed theoretical study. We have calculated graph–theoretic measures of functional network topology from numerical simulations of model networks. The effect of the form of local dynamics on the observed network state is quantified by examining the correlation between structural and functional connectivity. We document a profound and systematic dependence of the simulated functional connectivity patterns on the parameters controlling the dynamics. Importantly, we show that a weakly coupled oscillator theory explaining these correlations and their variation across parameter space can be developed. This theoretical development provides a novel way to characterize the mechanisms for the breakdown of functional connectivity in diseases through changes in local dynamics.
Collapse
Affiliation(s)
- Jaroslav Hlinka
- Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodarenskou vezi 271/2, 182 07 Prague 8, Czech Republic.
| | | |
Collapse
|