From synchronization to Lyapunov exponents and back

Antonio Politi, Francesco Ginelli, Serhiy Yanchuk, Yuri Maistrenko

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

The goal of this paper is twofold. In the first part we discuss a general approach to determine Lyapunov exponents from ensemble rather than time averages. The approach passes through the identification of locally stable and unstable manifolds (the Lyapunov vectors), thereby revealing an analogy with generalized synchronization. The method is then applied to a periodically forced chaotic oscillator to show that the modulus of the Lyapunov exponent associated to the phase dynamics increases quadratically with the coupling strength and it is therefore different from zero already below the onset of phase synchronization. The analytical calculations are carried out for a model, the generalized special flow, that we construct as a simplified version of the periodically forced Rossler oscillator. (c) 2006 Elsevier BX All rights reserved.

Original languageEnglish
Pages (from-to)90-101
Number of pages12
JournalPhysica. D, Nonlinear Phenomena
Volume224
Issue number1-2
Early online date7 Nov 2006
DOIs
Publication statusPublished - Dec 2006

Keywords

  • synchronization
  • Lyapunov exponents
  • coupled chaotic oscillators
  • phase synchronization
  • transition
  • systems
  • modes

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