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

Ernest Barreto, Brian Hunt, Edward Ott, and Paul So
Phys. Rev. E 77, 036107 – Published 6 March 2008

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.

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  • Received 7 August 2007

DOI:https://doi.org/10.1103/PhysRevE.77.036107

©2008 American Physical Society

Authors & Affiliations

Ernest Barreto1,*, Brian Hunt2, Edward Ott3, and Paul So1

  • 1Department of Physics & Astronomy, The Center for Neural Dynamics and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia 22030, USA
  • 2Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
  • 3Institute for Research in Electronics and Applied Physics, Department of Physics, and Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA

  • *ebarreto@gmu.edu

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Vol. 77, Iss. 3 — March 2008

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