Maximal lyapunov exponent and almost-sure stability for coupled two-degree-of-freedom stochastic systems

N. Sri Namachchivaya, H. J. Van Roessel, S. Talwar

Research output: Contribution to journalArticle

Abstract

In this paper, a perturbation approach is used to calculate the asymptotic growth rate of stochastically coupled two-degree-of-freedom systems. The noise is assumed to be white and of small intensity in order to calculate the explicit asymptotic formulas for the maximum Lyapunov exponent, The Lyapunov exponents and rotation number for each degree-of-freedom are obtained in the Appendix. The almost-sure stability or instability of the four-dimensional stochastic system depends on the sign of the maximum Lyapunov exponent. The results presented here match those presented by the first author and others using the method of stochastic averaging, where approximate ltŏ equations in amplitudes and phase are obtained in the sense of weak convergence.

Original languageEnglish (US)
Pages (from-to)446-452
Number of pages7
JournalJournal of Applied Mechanics, Transactions ASME
Volume61
Issue number2
DOIs
StatePublished - Jun 1994

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ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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