Maximal lyapunov exponent and rotation number for stochastically perturbed co-dimension two bifurcations

N. Sri Namachchivaya, S. Talwar

Research output: Contribution to journalArticle

Abstract

Almost-sure asymptotic stability of three- and four-dimensional co-dimension two dynamical systems under small intensity stochastic excitations is investigated. The method of stochastic averaging is used to derive a set of approximate Ito equations. These equations, along with their sample properties, are then examined to obtain the almost-sure stability conditions. The sample properties of the process are based on the boundary behavior of the associated scalar diffusion process of the amplitude Ito equations. The maximal Lyapunov exponent is calculated using the ergodic scalar diffusive process, which in turn yields the almost-sure stability conditions. This method is then applied to a linear, gyroscopic problem of a rotating shaft with a random loading.

Original languageEnglish (US)
Pages (from-to)349-372
Number of pages24
JournalJournal of Sound and Vibration
Volume169
Issue number3
DOIs
StatePublished - Jan 20 1994

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ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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