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Globally Coupled Oscillator Networks

In: Perspectives and Problems in Nolinear Science

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  • Eric Brown
  • Philip Holmes
  • Jeff Moehlis

Abstract

We study a class of permutation-symmetric globally-coupled, phase oscillator networks on N-dimensional tori. We focus on the effects of symmetry and of the forms of the coupling functions, derived from underlying Hodgkin-Huxley type neuron models, on the existence, stability, and degeneracy of phase-locked solutions in which subgroups of oscillators share common phases. We also estimate domains of attraction for the completely synchronized state. Implications for stochastically forced networks and ones with random natural frequencies are discussed and illustrated numerically. We indicate an application to modeling the brain structure locus coeruleus: an organ involved in cognitive control.

Suggested Citation

  • Eric Brown & Philip Holmes & Jeff Moehlis, 2003. "Globally Coupled Oscillator Networks," Springer Books, in: Ehud Kaplan & Jerrold E. Marsden & Katepalli R. Sreenivasan (ed.), Perspectives and Problems in Nolinear Science, chapter 5, pages 183-215, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-21789-5_5
    DOI: 10.1007/978-0-387-21789-5_5
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