Transition to Chaos in Continuous-Time Random Dynamical Systems

Zonghua Liu, Ying-Cheng Lai, Lora Billings, Ira B. Schwartz

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We consider situations where, in a continuous-time dynamical system, a nonchaotic attractor coexists with a nonattracting chaotic saddle, as in a periodic window. Under the influence of noise, chaos can arise. We investigate the fundamental dynamical mechanism responsible for the transition and obtain a general scaling law for the largest Lyapunov exponent. A striking finding is that the topology of the flow is fundamentally disturbed after the onset of noisy chaos, and we point out that such a disturbance is due to changes in the number of unstable eigendirections along a continuous trajectory under the influence of noise.

Original languageEnglish (US)
Number of pages1
JournalPhysical Review Letters
Volume88
Issue number12
DOIs
StatePublished - Jan 1 2002

    Fingerprint

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this