PMID: 11909463Mar 23, 2002Paper

Transition to chaos in continuous-time random dynamical systems

Physical Review Letters
Zonghua LiuI B Schwartz

Abstract

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.

References

Jan 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Y C Lai
Dec 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Y C LaiC Grebogi
Feb 13, 1989·Physical Review Letters·J M Deutsch, G Paladin
Mar 7, 1994·Physical Review Letters·A Maritan, J R Banavar
Oct 3, 1994·Physical Review Letters·S DawsonJ A Yorke
Dec 16, 1996·Physical Review Letters·T Yalçinkaya, Y C Lai

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Citations

Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xingang WangChoy Heng Lai
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Christian S RodriguesAlessandro P S de Moura
Apr 20, 2019·Physical Review. E·Jean-Régis Angilella
May 7, 2003·Physical Review Letters·Bin XuYounghae Do
Mar 5, 2004·Physical Review Letters·Xingang WangYing-Cheng Lai
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ying-Cheng LaiIra B Schwartz
Nov 7, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Bóris MarinEduardo Colli
Oct 15, 2020·Journal of the Royal Society, Interface·Yu MengCelso Grebogi
Jul 8, 2021·Journal of the Royal Society, Interface·Alan HastingsMary Lou Zeeman

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