Transition to chaos in continuous-time random dynamical systems

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

Research output: Contribution to journalArticleResearchpeer-review

24 Citations (Scopus)

Abstract

A continuous-time dynamical system in which a nonchaotic attractor coexists with a nonattracting chaotic saddle, was discussed. The fundamental dynamical mechanism responsible for the transition was investigated. A general scaling low for the largest Lyapunov exponent, was obtained. The topology of the flow was fundamentally disturbed after the onset of noisy chaos. It was found that such a disturbance was 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
StatePublished - 25 Mar 2002

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saddles
dynamical systems
chaos
disturbances
topology
trajectories
exponents
scaling

Cite this

Liu, Z., Billings, L., Schwartz, I. B., & Lai, Y. C. (2002). Transition to chaos in continuous-time random dynamical systems. Physical Review Letters, 88(12), 1241011-1241014. [124101].
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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Liu, Z, Billings, L, Schwartz, IB & Lai, YC 2002, 'Transition to chaos in continuous-time random dynamical systems', Physical Review Letters, vol. 88, no. 12, 124101, pp. 1241011-1241014.

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 journalArticleResearchpeer-review

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T1 - Transition to chaos in continuous-time random dynamical systems

AU - Liu, Zonghua

AU - Billings, Lora

AU - Schwartz, Ira B.

AU - Lai, Ying Cheng

PY - 2002/3/25

Y1 - 2002/3/25

N2 - A continuous-time dynamical system in which a nonchaotic attractor coexists with a nonattracting chaotic saddle, was discussed. The fundamental dynamical mechanism responsible for the transition was investigated. A general scaling low for the largest Lyapunov exponent, was obtained. The topology of the flow was fundamentally disturbed after the onset of noisy chaos. It was found that such a disturbance was due to changes in the number of unstable eigendirections along a continuous trajectory under the influence of noise.

AB - A continuous-time dynamical system in which a nonchaotic attractor coexists with a nonattracting chaotic saddle, was discussed. The fundamental dynamical mechanism responsible for the transition was investigated. A general scaling low for the largest Lyapunov exponent, was obtained. The topology of the flow was fundamentally disturbed after the onset of noisy chaos. It was found that such a disturbance was due to changes in the number of unstable eigendirections along a continuous trajectory under the influence of noise.

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JF - Physical Review Letters

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M1 - 124101

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Liu Z, Billings L, Schwartz IB, Lai YC. Transition to chaos in continuous-time random dynamical systems. Physical Review Letters. 2002 Mar 25;88(12):1241011-1241014. 124101.