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

• Main Authors: CHEW, L. Y., TING, Hian Ann, Christopher, LAI, C. H.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2005
• Subjects: Management Sciences and Quantitative Methods
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/1872; https://doi.org/10.1103/PhysRevE.72.036222
• Institution: Singapore Management University

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.