Transition to chaos in continuous-time random dynamical systems.
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.
Liu
Zonghua
Z
Department of Mathematics, Center for Systems Science and Engineering Research, Arizona State University, Tempe, Arizona 85287, USA.
Lai
Ying-Cheng
YC
Billings
Lora
L
Schwartz
Ira B
IB