Transition to Chaos in Continuous-Time Random Dynamical Systems

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

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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
Issue number12
StatePublished - 25 Mar 2002


Dive into the research topics of 'Transition to Chaos in Continuous-Time Random Dynamical Systems'. Together they form a unique fingerprint.

Cite this