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

TL;DR

This paper analyzes how synchronization emerges in complex networks composed of multiple interacting populations of heterogeneous oscillators, providing critical conditions for collective behavior onset with neurobiological applications.

Contribution

It introduces a framework for understanding synchronization in multi-population oscillator networks with heterogeneous frequencies and variable coupling strengths.

Findings

Derived the critical condition for synchronization onset.

Analyzed the case with Cauchy-Lorentz frequency distributions.

Applied results to neurobiological systems with interacting neuron populations.

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.