Chew LY, Ting C, Lai CH. Chaotic resonance: two-state model with chaos-induced escape over potential barrier.
Phys Rev E Stat Nonlin Soft Matter Phys 2005;
72:036222. [PMID:
16241563 DOI:
10.1103/physreve.72.036222]
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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.
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