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

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  • Hasegawa, Hideo

Abstract

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 a and b but also for τ while the stationary probability distribution function is independent of them where a and b denote magnitudes of multiplicative and additive noises, respectively, and τ 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 a, b and/or τ. 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.

Suggested Citation

  • Hasegawa, Hideo, 2013. "Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2532-2546.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:10:p:2532-2546
    DOI: 10.1016/j.physa.2013.01.052
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    Cited by:

    1. Zhou, Bingchang & McDonnell, Mark D., 2015. "Optimising threshold levels for information transmission in binary threshold networks: Independent multiplicative noise on each threshold," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 659-667.

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