Title: Transition to chaos in continuous-time random dynamical systems
Speaker: Zong-Hua Liu
Speaker Info: Arizona State U.
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The problem of noise-induced chaos is fundamental to understanding the interplay between stochasticity and nonlinearity, which is important for a variety of fields. In this talk, 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.Date: Friday, June 27, 2003