Dynamics of a network of phase oscillators with plastic couplings

Nekorkin, Vladimir I.; Кasatkin, D. V.

doi:10.1063/1.4951993

Cited by 15 publications

(13 citation statements)

References 8 publications

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“…Moreover, it was shown that all one-cluster solutions of splay type form an N − 2 dimensional family and thus give rise to infinitely many solutions the system can achieve. With this, we have generalized and extended the results reported in [7,19,35].…”

Section: Discussionsupporting

confidence: 56%

Multiclusters in Networks of Adaptively Coupled Phase Oscillators

Berner¹,

Schöll²,

Yanchuk³

2019

SIAM J. Appl. Dyn. Syst.

114

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Dynamical systems on networks with adaptive couplings appear naturally in realworld systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase oscillators inspired by neuronal networks with synaptic plasticity. One important behaviour of such systems reveals splitting of the network into clusters of oscillators with the same frequencies, where different clusters correspond to different frequencies. Starting from one-cluster solutions we provide existence criteria for multicluster solutions and present their explicit form. The phases of the oscillators within one cluster can be organized in different patterns: antipodal, double antipodal, and splay type. Interestingly, multi-clusters are shown to exist where different clusters exhibit different patterns. For instance, an antipodal cluster can coexist with a splay cluster. We also provide stability conditions for one-and multi-cluster solutions. These conditions, in particular, reveal a high level of multistability.

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Section: Discussionsupporting

confidence: 56%

Multiclusters in Networks of Adaptively Coupled Phase Oscillators

Berner¹,

Schöll²,

Yanchuk³

2019

SIAM J. Appl. Dyn. Syst.

114

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“…Various synchronization patterns are known, like cluster synchronization where the network splits into groups of synchronous elements [14], or partial synchronization patterns like chimera states where the system splits into coexisting domains of coherent (synchronized) and incoherent (desynchronized) states [15][16][17]. These patterns were also explored in adaptive networks [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Furthermore, adapting the network topology has also successfully been used to control cluster synchronization in delay-coupled networks [34].Another focus of recent research in network science are multilayer networks, which are systems interconnected through different types of links [35][36][37][38].…”

mentioning

confidence: 99%

“…Eq. (S1) has been widely used as a paradigmatic model for adaptive networks [18][19][20][21][22][23][24][25][26][27][28][29][30]. It generalizes the Kuramoto-Sakaguchi model with fixed coupling topology [90][91][92][93][94].…”

mentioning

confidence: 99%

“…For a single layer, Eq. (S1) has been studied numerically and analytically [18][19][20][21][22]24]. In particular, it was shown that starting from uniformly distributed random initial condition φ i ∈ [0, 2π), κ ij ∈ [−1, 1] the system can reach different frequency multi-cluster states with hierarchical structure depending on the parameters α and β.…”

mentioning

confidence: 99%

“…It is known that already the monoplex system (S1) possesses a huge variety of dynamical states such as multi-clusters with respect to frequency synchronization, chaotic attractors, and chimera-like states [20][21][22][23][24]. In this article we will focus on the simplest patterns, namely one-cluster states, and their generalization to the multiplex case.…”

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confidence: 99%

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Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

2020

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We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuro-and social sciences, as well as biology, engineering, and other disciplines. We show by theoretical analysis and computer simulations that multiplexing in a multi-layer network with symmetry can induce various stable phase cluster states in a situation where they are not stable or do not even exist in the single layer. Further, we develop a method for the analysis of Laplacian matrices of multiplex networks which allows for insight into the spectral structure of these networks enabling a reduction to the stability problem of single layers. We employ the multiplex decomposition to provide analytic results for the stability of the multilayer patterns. As local dynamics we use the paradigmatic Kuramoto phase oscillator, which is a simple generic model and has been successfully applied in the modeling of synchronization phenomena in a wide range of natural and technological systems.Complex networks are an ubiquitous paradigm in nature and technology, with a wide field of applications ranging from physics, chemistry, biology, neuroscience, to engineering and socio-economic systems. Of particular interest are adaptive networks, where the connectivity changes in time, for instance, the synaptic connections between neurons are adapted depending on the relative timing of neuronal spiking [1][2][3][4][5]. Similarly, chemical systems have been reported [6], where the reaction rates adapt dynamically depending on the variables of the system. Activity-dependent plasticity is also common in epidemics [7] and in biological or social systems [8]. Synchronization is an important feature of the dynamics in networks of coupled nonlinear oscillators [9][10][11][12][13]. Various synchronization patterns are known, like cluster synchronization where the network splits into groups of synchronous elements [14], or partial synchronization patterns like chimera states where the system splits into coexisting domains of coherent (synchronized) and incoherent (desynchronized) states [15][16][17]. These patterns were also explored in adaptive networks [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Furthermore, adapting the network topology has also successfully been used to control cluster synchronization in delay-coupled networks [34].Another focus of recent research in network science are multilayer networks, which are systems interconnected through different types of links [35][36][37][38]. A prominent example are social networks which can be described as groups of people with different patterns of contacts or interactions between them [39][40][41]. Other applications are communication, supply, and transportation networks, for instance power grids, subway networks, or airtraffic networks [42]. In neuroscience, multilayer networks represent for instance neurons in different areas of the brain, neurons connected either by a chemical link or by an electrical synapsis, or...

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Introduction

Berner

2021

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

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Dynamics of a network of phase oscillators with plastic couplings

Cited by 15 publications

References 8 publications

Multiclusters in Networks of Adaptively Coupled Phase Oscillators

Multiclusters in Networks of Adaptively Coupled Phase Oscillators

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

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