The effect of topology on organization of synchronous behavior in dynamical networks with adaptive couplings

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

doi:10.1140/epjst/e2018-800077-7

Cited by 23 publications

(21 citation statements)

References 30 publications

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“…More specifically, we study rings of nonlocally coupled oscillators based on the Kuramoto-Sakaguchi model [26,27] with an additional adaptation dynamics of the coupling weights. For an all-to-all coupling topology similar models have been recently a e-mail: rico.berner@physik.tu-berlin.de studied [28][29][30][31][32][33][34][35][36][37], but very little is known about the dynamics of these systems if the base topology is more complex [38]. On globally coupled networks, adaptive Kuramoto-Sakaguchi type models have been shown to exhibit diverse complex dynamical behavior.…”

Section: Introductionmentioning

confidence: 99%

Solitary states in adaptive nonlocal oscillator networks

Berner

Polanska

Schöll

et al. 2020

Eur. Phys. J. Spec. Top.

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In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the phase-locked solutions, the rotating waves, we provide a rigorous stability analysis. This analysis shows a strong dependence of their stability on the coupling structure and the wavenumber which is a remarkable difference to an all-to-all coupled network. Despite the fact that solitary states have been observed in a plethora of dynamical systems, the mechanisms behind their emergence were largely unaddressed in the literature. Here, we show how solitary states emerge due to the adaptive feature of the network and classify several bifurcation scenarios in which these states are created and stabilized.

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Section: Introductionmentioning

confidence: 99%

Solitary states in adaptive nonlocal oscillator networks

Berner

Polanska

Schöll

et al. 2020

Eur. Phys. J. Spec. Top.

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“…Moreover, adaptive networks have been reported for chemical [67,68], epidemic [69], biological [70], transport [71], and social systems [72,73]. A paradigmatic example of adaptively coupled phase oscillators has recently attracted much attention [12,41,[74][75][76][77][78][79][80][81], and it appears to be useful for predicting and describing phenomena in more realistic and detailed models [82][83][84][85]. Systems of phase oscillators are important for understanding synchronization phenomena in a wide range of applications [86][87][88].…”

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confidence: 99%

Desynchronization Transitions in Adaptive Networks

et al. 2021

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Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In this Letter, we develop the master stability approach for a large class of adaptive networks. This approach allows for reducing the synchronization problem for adaptive networks to a low-dimensional system, by decoupling topological and dynamical properties. We show how the interplay between adaptivity and network structure gives rise to the formation of stability islands. Moreover, we report a desynchronization transition and the emergence of complex partial synchronization patterns induced by an increasing overall coupling strength. We illustrate our findings using adaptive networks of coupled phase oscillators and FitzHugh-Nagumo neurons with synaptic plasticity.

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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%

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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The effect of topology on organization of synchronous behavior in dynamical networks with adaptive couplings

Cited by 23 publications

References 30 publications

Solitary states in adaptive nonlocal oscillator networks

Solitary states in adaptive nonlocal oscillator networks

Desynchronization Transitions in Adaptive Networks

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

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