Hierarchical frequency clusters in adaptive networks of phase oscillators

Berner, Rico; Fialkowski, Jan; Кasatkin, D. V.; Nekorkin, Vladimir I.; Yanchuk, Serhiy; Schöll, Eckehard

doi:10.1063/1.5097835

Cited by 50 publications

(74 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…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. The frequency multi-clusters in turn consist of several one-clusters which determine the existence and stability of the former [23]. Therefore, these one-cluster states (with identical frequency, but different phase distributions) constitute the building blocks of adaptively coupled phase oscillators.…”

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.…”

mentioning

confidence: 99%

“…Moreover, in contrast to the other examples the phase distribution between the layers does not agree, ψ 1 = ψ 2 . For the monoplex case, it has been shown that double antipodal states are unstable for any set of parameters [23]. Hence, finding stable double antipodal states which interact through the duplex structure is unexpected.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

2020

Self Cite

View full text Add to dashboard Cite

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...

show abstract