Transition to Chaos in Continuous-Time Random Dynamical Systems

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

Research output: Contribution to journalArticleResearchpeer-review

2 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
Number of pages1
JournalPhysical Review Letters
Volume88
Issue number12
DOIs
StatePublished - 1 Jan 2002

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dynamical systems
chaos
saddles
scaling laws
disturbances
topology
trajectories
exponents

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

In: Physical Review Letters, Vol. 88, No. 12, 01.01.2002.

Research output: Contribution to journalArticleResearchpeer-review

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AB - 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.

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