Chaotic behavior in differential equations driven by a Brownian motion

Kening Lu, Qiu-Dong Wang

Research output: Contribution to journalArticle

14 Citations (Scopus)

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
StatePublished - Nov 15 2011

Fingerprint

Brownian movement
Chaotic Behavior
Brownian motion
Differential equations
Topological Horseshoe
Differential equation
Wiener Space
Duffing Equation
Homoclinic Orbit
Sample Path
Pendulum
Pendulums
Saddlepoint
Ordinary differential equations
Forcing
Ordinary differential equation
Orbits
Branch
Fixed point

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

Cite this

Chaotic behavior in differential equations driven by a Brownian motion. / Lu, Kening; Wang, Qiu-Dong.

In: Journal of Differential Equations, Vol. 251, No. 10, 15.11.2011, p. 2853-2895.

Research output: Contribution to journalArticle

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