Extreme Sensitivity to Detuning for Globally Coupled Phase Oscillators

Peter Ashwin, Oleksandr Burylko, Yuri Maistrenko, and Oleksandr Popovych
Phys. Rev. Lett. 96, 054102 – Published 6 February 2006

Abstract

We discuss the sensitivity of a population of coupled oscillators to differences in their natural frequencies, i.e., to detuning. We argue that for three or more oscillators, one can get great sensitivity even if the coupling is strong. For N globally coupled phase oscillators we find there can be bifurcation to extreme sensitivity, where frequency locking can be destroyed by arbitrarily small detuning. This extreme sensitivity is absent for N=2, appears at isolated parameter values for N=3 and N=4, and can appear robustly for open sets of parameter values for N5 oscillators.

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  • Received 4 August 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.054102

©2006 American Physical Society

Authors & Affiliations

Peter Ashwin1, Oleksandr Burylko2, Yuri Maistrenko2,3, and Oleksandr Popovych3

  • 1Department of Mathematical Sciences, University of Exeter, Exeter EX4 4QE, United Kingdom
  • 2Institute of Mathematics, National Academy of Sciences of Ukraine, 01601 Kyiv, Ukraine
  • 3Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre Jülich, 52425 Jülich, Germany

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Issue

Vol. 96, Iss. 5 — 10 February 2006

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