Stochastic resonance in second-order and underdamped asymmetric bistable system

Abstract

The phenomenon of stochastic resonance (SR) in a second-order and underdamped asymmetric bistable system is investigated. The second-order asymmetric bistable system with Gauss white noise is stochastically equivalent to two-dimensional Markovian process, and the exact expression of the signal-to-noise ratio (SNR) of system response in the presence of weak periodic driving force is obtained under the adiabatic condition and the theory of two-state model intensities. The influences of the damping parameter, asymmetry constant r and the Gaussian white noises on the SNR are discussed. The present calculation results show that, the increase of static asymmetry r and damping parameter γ can restrain the SR phenomenon appears. However, the increase of signal amplitude A can enhance SR.