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 Citations (Scopus)

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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dynamical systems
chaos
saddles
scaling laws
disturbances
topology
trajectories
exponents

Cite this

Liu, Zonghua ; Billings, Lora ; Schwartz, Ira B. ; Lai, Ying Cheng. / Transition to Chaos in Continuous-Time Random Dynamical Systems. In: Physical Review Letters. 2002 ; Vol. 88, No. 12. pp. 1241011-1241014.
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Transition to Chaos in Continuous-Time Random Dynamical Systems. / Liu, Zonghua; Billings, Lora; Schwartz, Ira B.; Lai, Ying Cheng.

In: Physical Review Letters, Vol. 88, No. 12, 124101, 25.03.2002, p. 1241011-1241014.

Research output: Contribution to journalArticle

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AU - Schwartz, Ira B.

AU - Lai, Ying Cheng

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