Synchronization of heterogeneous oscillator populations in response to weak and strong coupling

Wilson, Dan; Faramarzi, Sadegh; Moehlis, Jeff; Tinsley, Mark R.; Showalter, Kenneth

doi:10.1063/1.5049475

Cited by 23 publications

(8 citation statements)

References 59 publications

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“…We illustrate one possible realization of this case and its realworld relevance with experimentally well-accessible chemical relaxation oscillators [22][23][24], that show qualitatively identical behavior to biological nerve and heart cells [25][26][27][28][29][30][31]. The oscillators are based on the Belousov-Zhabotinsky reaction and their dynamics are well-captured in the two-component non-dimensionalized Zhabotinsky-Buchholtz-Kiyatkin-Epstein (ZBKE) model [23,32,33]:…”

Section: Modelsmentioning

confidence: 96%

Chimera States on a Ring of Strongly Coupled Relaxation Oscillators

Rode

Totz

Fengler

et al. 2019

Front. Appl. Math. Stat.

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Weakly coupled oscillators can exhibit seemingly incongruous synchronization patterns comprised of coherent and incoherent spatial domains known as chimera states. However, the weak coupling approximation is invalid when the characteristic phase response curve of an oscillator does not scale linearly with the coupling strength and instead changes its shape. In chemical experiments with photo-coupled relaxation oscillators, we find that beyond weak coupling chimera patterns consist of different coexisting cluster states. Numerical modeling reveals that the observed cluster states result from a phase-dependent excitability that is also commonly observed in neural tissue and cardiac pacemaker cells.

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Section: Modelsmentioning

confidence: 96%

Chimera States on a Ring of Strongly Coupled Relaxation Oscillators

Rode

Totz

Fengler

et al. 2019

Front. Appl. Math. Stat.

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“…In general, the intrinsic dynamics of the nodes are not necessarily the same. Such is the case, for example, of networks of oscillators, in which the intrinsic frequency of the nodes is not identical [48]. We refer to such networks as heterogenous.…”

Section: Synchronization In Heterogeneous Network Using Strong Interconnectionsmentioning

confidence: 99%

Lyapunov-based synchronization of networked systems: From continuous-time to hybrid dynamics

Maghenem

Lorı́a

Panteley

2020

Annual Reviews in Control

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Synchronization pertains to the property of interconnected systems according to which their dynamic behavior is coordinated in an appropriate sense. That is to say, some of their state variables, or functions of the latter for that matter, converge to each other. Synchronization may occur naturally or may be induced, controlled, and it may be present between two systems or among a large number. In the latter case, it is convenient to speak of a network of interconnected systems. Understanding synchronization, and how to control it, is an important paradigm as it is present in a variety of scenarios. These involve, e.g., networks of technological systems (robots and vehicles of different kinds), social networks (by which people exchange opinions and agree, or not), networks of biological systems (uni or pluricellular), etc. Owing to the context, the mathematical models to describe such networks and to define synchronization formally, varies dramatically. Ordinary continuous-time or discrete-time models for which modern control theory and Lyapunov stability theory are tailored result inappropriate to incorporate hybrid phenomena that intervene in the network. These may stem from sudden topology changes, the use of digital or intermittent control strategies, the presence of impacts in the intrinsic dynamics of the nodes, etc. In this invited paper, we give an overview of synchronization control problems, mostly of cooperative control of networks of autonomous vehicles (based on continuous-time models). For that matter, the first part of the paper focuses on the main contributions of [1]. Then, we give further perspectives on what we consider significant open problems on synchronization of hybrid systems and hybrid networks.

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“…Mathematical analysis and control of oscillatory dynamical systems is a widely studied problem with relevant applications to neurological brain rhythms [37], [20], [26], circadian physiology [11], [3], [48], and various other physical and chemical systems [50], [13], [45], [62], [66]. Given the high dimensionality and sheer complexity of many oscillatory dynamical systems, model reduction is often a necessary first step in their analysis.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of Oscillation Timing and Entrainment Using Large Magnitude Inputs: An Adaptive Phase-Amplitude-Coordinate-Based Approach

Wilson¹

2021

SIAM J. Appl. Dyn. Syst.

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Given the high dimensionality and underlying complexity of many oscillatory dynamical systems, phase reduction is often an imperative first step in control applications where oscillation timing and entrainment are of interest. Unfortunately, most phase reduction frameworks place restrictive limitations on the magnitude of allowable inputs, limiting the practical utility of the resulting phase reduced models in many situations. In this work, motivated by the search for control strategies to hasten recovery from jet-lag caused by rapid travel through multiple time zones, the efficacy of the recently developed adaptive phase-amplitude reduction is considered for manipulating oscillation timing in the presence of a large magnitude entraining stimulus. The adaptive phase-amplitude reduced equations allow for a numerically tractable optimal control formulation and the associated optimal stimuli significantly outperform those resulting from from previously proposed optimal control formulations. Additionally, a data-driven technique to identify the necessary terms of the adaptive phase-amplitude reduction is proposed and validated using a model describing the aggregate oscillations of a large population of coupled limit cycle oscillators. Such data-driven model reduction algorithms are essential in situations where the underlying model equations are either unreliable or unavailable.

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Synchronization of heterogeneous oscillator populations in response to weak and strong coupling

Cited by 23 publications

References 59 publications

Chimera States on a Ring of Strongly Coupled Relaxation Oscillators

Chimera States on a Ring of Strongly Coupled Relaxation Oscillators

Lyapunov-based synchronization of networked systems: From continuous-time to hybrid dynamics

Optimal Control of Oscillation Timing and Entrainment Using Large Magnitude Inputs: An Adaptive Phase-Amplitude-Coordinate-Based Approach

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