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.
MSU Digital Commons Citation
Liu, Zonghua; Lai, Ying-Cheng; Billings, Lora; and Schwartz, Ira B., "Transition to Chaos in Continuous-Time Random Dynamical Systems" (2002). Department of Mathematical Sciences Faculty Scholarship and Creative Works. 20.
Liu, Z., Lai, Y. C., Billings, L., & Schwartz, I. B. (2002). Transition to chaos in continuous-time random dynamical systems. Phys Rev Lett, 88(12), 124101. doi:10.1103/PhysRevLett.88.124101