Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators

Abstract

The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a given population are heterogeneous in that their natural frequencies are drawn from a given distribution, and each population has its own such distribution. The coupling among the oscillators is global, however, we permit the coupling strengths between the members of different populations to be separately specified. We determine the critical condition for the onset of coherent collective behavior, and develop the illustrative case in which the oscillator frequencies are drawn from a set of (possibly different) Cauchy-Lorentz distributions. One motivation is drawn from neurobiology, in which the collective dynamics of several interacting populations of oscillators (such as excitatory and inhibitory neurons and glia) are of interest.

arXiv commentThe original was replaced with a version that has been accepted to Phys. Rev. E. The new version has the same content, but the title, abstract, and the introductory text have been revised

References in corpus (11)

• Community structure in social and biological networks
• Finding and evaluating community structure in networks
• Synchronization reveals topological scales in complex networks
• Layered Complex Networks
• Chimera States in a Ring of Nonlocally Coupled Oscillators
• Synchronization of two interacting populations of oscillators
• Synchronization processes in complex networks
• Averaged equations for Josephson junction series arrays with LRC load
• Synchronization in large directed networks of coupled phase oscillators
• Optimization of synchronization in gradient clustered networks
• The Onset of Synchronization in Systems of Globally Coupled Chaotic and Periodic Oscillators

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