Chaos Resonance: Two-State Model with Chaos-Induced Escape over Potential Barrier

Publication Type

Journal Article

Publication Date

2005

Abstract

We consider the resonant effects of chaotic fluctuations on a strongly damped particle in a bistable potential driven by weak sinusoidal perturbation. We derive analytical expressions of chaos-induced transition rate between the neighboring potential wells based on the inhomogeneous Smoluchowski equation. Our first-order analysis reveals that the transition rate has the form of the Kramers escape rate except for a perturbed prefactor. This modification to the prefactor is found to arise from the statistical asymmetry of the chaotic noise. By means of the two-state model and the chaos-induced transition rate, we arrive at an analytical expression of the signal-to-noise ratio (SNR). Our first-order SNR shows that chaotic resonance can correspond directly to stochastic resonance.

Discipline

Management Sciences and Quantitative Methods

Research Areas

Finance

Publication

Physical Review E

Volume

72

Issue

3

First Page

1

Last Page

13

ISSN

1063-651X

Identifier

10.1103/PhysRevE.72.036222

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