Almost-sure asymptotic stability of a general four-dimensional system driven by real noise

M. M. Doyle, N. Sri Namachchivaya

Research output: Contribution to journalArticlepeer-review

Abstract

In the first part of this paper, we construct an asymptotic expansion for the maximal Lyapunov exponent, the exponential growth rate of solutions to a linear stochastic system, and the rotation numbers for a general four-dimensional dynamical system driven by a small-intensity real noise process. Stability boundaries are obtained provided the natural frequencies are noncommensurable and the infinitesimal generator associated with the noise process has an isolated simple zero eigenvalue. This work is an extension of the work of Sri Namachchivaya and Van Roessel and is general in the sense that general stochastic perturbations of nonautonomous systems with two noncommensurable natural frequencies are considered.

Original languageEnglish (US)
Pages (from-to)525-552
Number of pages28
JournalJournal of Statistical Physics
Volume75
Issue number3-4
DOIs
StatePublished - May 1 1994

Keywords

  • Itô equations
  • Lyapunov exponents
  • almost-sure asymptotic stability
  • rotation numbers

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Almost-sure asymptotic stability of a general four-dimensional system driven by real noise'. Together they form a unique fingerprint.

Cite this