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

physical review. e, statistical, nonlinear and soft matter physics

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