Fast transition to chaos in a ring of unidirectionally coupled oscillators

Details Fast transition to chaos in a ring of unidirectionally coupled oscillators Fast transition to chaos in a ring of unidirectionally coupled oscillators

2010-11-22

arxiv.org/abs/1011.4786v1

Mathematics

Dynamical Systems

Scientific paper

In this paper we study the destabilization mechanism in a ring of unidirectionally coupled oscillators. We derive an amplitude equation of Ginzburg-Landau type that describes the destabilization of the stationary state for systems with a large number of oscillators. Based on this amplitude equation, we are able to provide an explanation for the fast transition to chaos (or hyperchaos) that can be observed in such systems. We show that the parameter interval, where the transition from a stable periodic state to chaos occurs, scales like the inverse square of the number of oscillators in the ring. In particular, for a sufficiently large number of oscillators a practically immediate transition to chaos can be observed. The results are illustrated by a numerical study of a system of unidirectionally coupled Duffing oscillators.

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