Transition to Chaos in Continuous-Time Random Dynamical Systems

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

Research output: Contribution to journalArticle

24 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
Article number124101
Pages (from-to)1241011-1241014
Number of pages4
JournalPhysical Review Letters
Volume88
Issue number12
DOIs
StatePublished - 25 Mar 2002

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