Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

N. Sri Namachchivaya, H. J. Van Roessel

Research output: Contribution to journalArticle

Abstract

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.

Original languageEnglish (US)
Pages (from-to)549-567
Number of pages19
JournalJournal of Statistical Physics
Volume71
Issue number3-4
DOIs
StatePublished - May 1993

Keywords

  • almost-sure stability
  • ItÔ equations
  • Lyapunov exponents
  • rotation numbers
  • stochastic averaging

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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