TY - JOUR
T1 - Transition to Chaos in Continuous-Time Random Dynamical Systems
AU - Liu, Zonghua
AU - Lai, Ying-Cheng
AU - Billings, Lora
AU - Schwartz, Ira B.
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.88.124101
DO - 10.1103/PhysRevLett.88.124101
M3 - Article
AN - SCOPUS:85038346858
SN - 0031-9007
VL - 88
SP - 4
JO - Physical Review Letters
JF - Physical Review Letters
IS - 12
ER -