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Fast transition to chaos in a ring of unidirectionally coupled oscillators

Please always quote using this URN:urn:nbn:de:0296-matheon-8200
  • 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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Metadaten
Author:Serhiy Yanchuk, Przemyslaw Perlikowski, Matthias Wolfrum, Andrzej Stefanski, Tomasz Kapitaniak
URN:urn:nbn:de:0296-matheon-8200
Referee:Alexander Mielke
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/04/29
Release Date:2011/04/29
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C15 Nonlinear oscillations, coupled oscillators
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C23 Bifurcation [See also 37Gxx]
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C28 Complex behavior, chaotic systems [See also 37Dxx]
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Gxx Local and nonlocal bifurcation theory [See also 34C23, 34K18] / 37G35 Attractors and their bifurcations
Preprint Number:785
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