Synchronization of phase-coupled oscillators with plastic coupling strength

Gushchin, Andrey; Mallada, Enrique; Tang, Ao

doi:10.1109/ita.2015.7309003

Cited by 13 publications

(19 citation statements)

References 28 publications

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“…The parameter α can be considered as a phase-lag of the interaction [46]. System (1.1)-(1.2) has attracted a lot of attention recently [26,6,7,25,35,19,39,50,45,10], since it is a first choice paradigmatic model for the modeling of the dynamics of adaptive networks. In particular, it generalizes the Kuramoto (or Kuramoto-Sakaguchi) model with fixed κ [4,28,37,49,40].…”

mentioning

confidence: 99%

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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confidence: 99%

Multiclusters in Networks of Adaptively Coupled Phase Oscillators

Berner¹,

Schöll²,

Yanchuk³

2019

SIAM J. Appl. Dyn. Syst.

114

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“…Another way, is to express the dynamics of the system using directly (η, ω, V ) variables, similarly as in [38]. However, we do not adopt this approach here in order to better contrast our results with others in the literature on oscillator synchronization that are mostly working with (θ, ω, V ) coordinates [14], [32], [27], [20].…”

Section: Remarkmentioning

confidence: 99%

“…which arises in oscillator networks with so-called plastic coupling strength ([27], [20], [22]) and in the context of flocking with state dependent sensing ( [27], [16], [32]). Although stability analysis of equilibria have been carried out for these systems, the investigation of the methods proposed in this paper in those contexts is still unexplored and deserves attention.…”

Section: Remarkmentioning

confidence: 99%

A modular design of incremental Lyapunov functions for microgrid control with power sharing

Persis

Monshizadeh

2016

2016 European Control Conference (ECC)

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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].…”

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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].…”

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confidence: 99%

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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Synchronization of phase-coupled oscillators with plastic coupling strength

Cited by 13 publications

References 28 publications

Multiclusters in Networks of Adaptively Coupled Phase Oscillators

Multiclusters in Networks of Adaptively Coupled Phase Oscillators

A modular design of incremental Lyapunov functions for microgrid control with power sharing

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

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