Quasipotential approach to critical scaling in noise-induced chaos

Tamás Tél, Ying Cheng Lai

Research output: Contribution to journalArticle

20 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
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume81
Issue number5
DOIs
Publication statusPublished - May 19 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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