Chaos Resonance: Two-State Model with Chaos-Induced Escape over Potential Barrier
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.
Management Sciences and Quantitative Methods
Physical Review E
CHEW, L. Y.; TING, Hian Ann, Christopher; and LAI, C. H..
Chaos Resonance: Two-State Model with Chaos-Induced Escape over Potential Barrier. (2005). Physical Review E. 72, (3), 1-13. Research Collection Lee Kong Chian School Of Business.
Available at: http://ink.library.smu.edu.sg/lkcsb_research/1872