Scaling laws for noise-induced superpersistent chaotic transients

Younghae Do, Ying-Cheng Lai

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

A superpersistent chaotic transient is characterized by the following scaling law for its average lifetime: τ ∼ exp[C(p-p c) ], where C>0 and α>0 are constants, p > p c is a bifurcation parameter, and p c is its critical value. As p approaches p c from above, the exponent in the exponential dependence diverges, leading to an extremely long transient lifetime. Historically the possibility of such transient raised the question of whether asymptotic attractors are relevant to turbulence. Here we investigate the phenomenon of noise-induced superpersistent chaotic transients. In particular, we construct a prototype model based on random maps to illustrate this phenomenon. We then approximate the model by stochastic differential equations and derive the scaling laws for the transient lifetime versus the noise amplitude e for both the subcritical (p < p c) and the supercritical (p > p c) cases. Our results are the following. In the subcritical case where a chaotic attractor exists in the absence of noise, noise-induced transients can be more persistent in the following sense of double-exponential and algebraic scaling: τ ∼exp[K 0exp(K 1ε )] for small noise amplitude ε, where K 0>0, K 1>0, and γ > 0 are constants. The longevity of the transient lifetime in this case is striking. For the supercritical case where there is already a superpersistent chaotic transient, noise can significantly reduce the transient lifetime. These results add to the understanding of the interplay between random and deterministic chaotic dynamics with surprising physical implications.

Original languageEnglish (US)
Article number046208
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume71
Issue number4
DOIs
StatePublished - Apr 2005

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Scaling Laws
scaling laws
life (durability)
Lifetime
Random Maps
differential equations
turbulence
prototypes
Chaotic Attractor
exponents
Chaotic Dynamics
Diverge
scaling
Stochastic Equations
Critical value
Attractor
Turbulence
Bifurcation
Exponent
Scaling

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Scaling laws for noise-induced superpersistent chaotic transients. / Do, Younghae; Lai, Ying-Cheng.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 71, No. 4, 046208, 04.2005.

Research output: Contribution to journalArticle

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