Quasipotential approach to critical scaling in noise-induced chaos

Tamas Tel, Ying-Cheng Lai

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

When a dynamical system exhibits transient chaos and a nonchaotic attractor, as in a periodic window, noise can induce a chaotic attractor. In particular, when the noise amplitude exceeds a critical value, the largest Lyapunov exponent of the attractor of the system starts to increase from zero. While a scaling law for the variation of the Lyapunov exponent with noise was uncovered previously, it is mostly based on numerical evidence and a heuristic analysis. This paper presents a more general approach to the scaling law, one based on the concept of quasipotentials. Besides providing deeper insights into the problem of noise-induced chaos, the quasipotential approach enables previously unresolved issues to be addressed. The fractal properties of noise-induced chaotic attractors and applications to biological systems are also discussed.

Original languageEnglish
Article number056208
Number of pages8
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume81
Issue number5
DOIs
Publication statusPublished - May 2010

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