Transition to chaos in continuous-time random dynamical systems

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

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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
Number of pages4
JournalPhysical Review Letters
Issue number12
Publication statusPublished - 25 Mar 2002


  • high-dimensional chaos
  • synchronization
  • fluctuations
  • noise


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