Phys. Rev. E, 66 (2002) 035201(R). doi:10.1103/PhysRevE.66.035201

Infinities of stable periodic orbits in systems of coupled oscillators

Peter Ashwin(1) A.M.Rucklidge(2) Rob Sturman(2).
(1) School of Mathematical Sciences, Laver Building,
University of Exeter, Exeter EX4 4QE, UK

(2) Department of Applied Mathematics,
University of Leeds, Leeds, LS2 9JT, UK

Abstract. We consider the dynamical behaviour 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.

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