Chaos in Symmetric Phase Oscillator Networks

Christian Bick, Marc Timme, Danilo Paulikat, Dirk Rathlev, and Peter Ashwin
Phys. Rev. Lett. 107, 244101 – Published 9 December 2011

Abstract

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization so far has been found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic dynamics, but also chaotically fluctuating order parameters. Our findings imply that neither inhomogeneities nor amplitude variations are necessary to obtain chaos; i.e., nonlinear interactions of phases give rise to the necessary instabilities.

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  • Received 9 May 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.244101

© 2011 American Physical Society

Authors & Affiliations

Christian Bick1,2, Marc Timme1,3, Danilo Paulikat3, Dirk Rathlev3, and Peter Ashwin4

  • 1Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37073 Göttingen, Germany
  • 2Institute for Mathematics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
  • 3Faculty of Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
  • 4Mathematics Research Institute, University of Exeter, Exeter EX4 4QF, United Kingdom

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Issue

Vol. 107, Iss. 24 — 9 December 2011

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