Chaotic behavior in differential equations driven by a Brownian motion

Kening Lu, Qiu-Dong Wang

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

In this paper, we investigate the chaotic behavior of ordinary differential equations with a homoclinic orbit to a saddle fixed point under an unbounded random forcing driven by a Brownian motion. We prove that, for almost all sample paths of the Brownian motion in the classical Wiener space, the forced equation admits a topological horseshoe of infinitely many branches. This result is then applied to the randomly forced Duffing equation and the pendulum equation.

Original languageEnglish (US)
Pages (from-to)2853-2895
Number of pages43
JournalJournal of Differential Equations
Volume251
Issue number10
DOIs
Publication statusPublished - Nov 15 2011

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Keywords

  • Brownian motion
  • Cantor sets
  • Chaotic behavior
  • Duffing equation
  • Pendulum equation
  • Random melnikov function
  • Topological horseshoe
  • Unbounded stochastic forcing
  • Wiener shift

ASJC Scopus subject areas

  • Analysis

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