Cluster Synchronization in Multilayer Networks: A Fully Analog Experiment with 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>L</mml:mi><mml:mi>C</mml:mi></mml:math>
 Oscillators with Physically Dissimilar Coupling

Blaha, Karen; Huang, Ke; Rossa, Fabio Della; Pecora, Louis M.; Hossein‐Zadeh, Mani; Sorrentino, Francesco

doi:10.1103/physrevlett.122.014101

Cited by 37 publications

(24 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, in ref. 31 , a 'multilayer network' has connections of different types but nodes all of the same type. Here we consider the most general situation for which both nodes and connections can be of different types, with the case of ref.…”

Section: Resultsmentioning

confidence: 99%

“…Here we consider the most general situation for which both nodes and connections can be of different types, with the case of ref. 31 remaining a special case of multilayer network.…”

Section: Resultsmentioning

confidence: 99%

“…Reference 37 introduced a mathematical model for the time evolution of a multiplex network. Following previous studies of synchronization in different instances of multilayer networks 8,15,16,31,37 , next we provide a general set of equations that describe the dynamics of a multilayer network. First we define the sets of nodes and of connections (or interactions) of a multilayer network.…”

Section: Resultsmentioning

confidence: 99%

“…When equitable partitions arise from symmetry, a rigorous, group theory-based framework exists to analyze the stability of cluster synchronization in simple networks 20,21,24 . However, cluster synchronization in multilayer networks has not been studied other than in a recent paper, which focused on experimental observations on a special multilayer network composed of nodes all of the same type 31 .…”

mentioning

confidence: 99%

See 3 more Smart Citations

Symmetries and cluster synchronization in multilayer networks

et al. 2020

Self Cite

View full text Add to dashboard Cite

Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the emergence of cluster synchronization in these networks. We distinguish between independent layer symmetries, which occur in one layer and are independent of the other layers, and dependent layer symmetries, which involve nodes in different layers. We study stability of the cluster synchronous solution by decoupling the problem into a number of independent blocks and assessing stability of each block through a Master Stability Function. We see that blocks associated with dependent layer symmetries have a different structure to the other blocks, which affects the stability of clusters associated with these symmetries. Finally, we validate the theory in a fully analog experiment in which seven electronic oscillators of three kinds are connected with two kinds of coupling.

show abstract

Section: Resultsmentioning

confidence: 99%

“…Here we consider the most general situation for which both nodes and connections can be of different types, with the case of ref. 31 remaining a special case of multilayer network.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Symmetries and cluster synchronization in multilayer networks

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…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 the modular connectivity structure of brain regions [43][44][45][46][47][48][49][50][51]. A special case of multilayer networks are multiplex topologies, where each layer contains the same set of nodes, and only pairwise connections between corresponding nodes from neighbouring layers exist [52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71].In spite of the lively interest in the topic of adaptive networks, little is known about the interplay of adaptively coupled groups of networks [25,72,73]. Such adaptive multilayer or multiplex networks appear naturally in neuronal networks, e.g., in interacting neuron populations with plastic synapses but different plasticity rules within each population [74,75], or affected by different mechanisms of plasticity [76], or the transport of metabolic resources [77].…”

mentioning

confidence: 99%

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

2020

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

Introduction

Berner

2021

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

View full text Add to dashboard Cite

Cluster Synchronization in Multilayer Networks: A Fully Analog Experiment with LC Oscillators with Physically Dissimilar Coupling

Cited by 37 publications

References 56 publications

Symmetries and cluster synchronization in multilayer networks

Symmetries and cluster synchronization in multilayer networks

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

Introduction

Contact Info

Product

Resources

About