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Infinities of stable periodic orbits in systems of coupled oscillators

Peter Ashwin, Alastair M. Rucklidge, and Rob Sturman
Phys. Rev. E 66, 035201(R) – Published 3 September 2002
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Abstract

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor.

  • Received 14 January 2002

DOI:https://doi.org/10.1103/PhysRevE.66.035201

©2002 American Physical Society

Authors & Affiliations

Peter Ashwin*

  • School of Mathematical Sciences, Laver Building, University of Exeter, Exeter EX4 4QE, United Kingdom

Alastair M. Rucklidge and Rob Sturman

  • Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

  • *Email address: P.Ashwin@ex.ac.uk
  • Email address: A.M.Rucklidge@leeds.ac.uk
  • Email address: rsturman@amsta.leeds.ac.uk

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Issue

Vol. 66, Iss. 3 — September 2002

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