title: Chaotic resonance: two-state model with chaos-induced escape over potential barrier.
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.
authors.affiliation: School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637616.
authors.forename: L Y
authors.initials: LY
authors.lastname: Chew
authors.forename: Christopher
authors.initials: C
authors.lastname: Ting
authors.forename: C H
authors.initials: CH
authors.lastname: Lai