Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

We have studied the stochastic resonance (SR) of bistable systems coupled to a bath with a nonlinear system–bath interaction, by using the microscopic, generalized Caldeira–Leggett (CL) model. The adopted CL model yields the non-Markovian Langevin equation with nonlinear dissipation and state-dependent (multiplicative) diffusion which preserve the fluctuation–dissipation relation (FDR). Results of our simulations are given as follows: (1) the spectral power amplification (SPA) exhibits SR not only for aa and bb but also for ττ while the stationary probability distribution function is independent of them where aa and bb denote magnitudes of multiplicative and additive noises, respectively, and ττ expresses the relaxation time of Ornstein–Uhlenbeck (OU) colored noise; (2) the SPA for coexisting additive and multiplicative noises has a single-peak but two-peak structure as functions of aa, bb and/or ττ. Results (1) and (2) are qualitatively different from previous ones obtained by phenomenological Langevin models where the FDR is not held or indefinite. These show an importance of the FDR in a study on SR of open bistable systems.

► Stochastic resonance of open bistable systems is studied by a microscopic model.
► The derived Langevin equation preserves the fluctuation–dissipation relation.
► Stochastic resonance is realized for the relaxation time of colored noise.
► Our results are different from previous ones obtained by phenomenological models.