Stochastic resonance in bistable systems driven by harmonic noise

2003

We analyze stochastic resonance in systems driven by non-Gaussian noises. For the bistable double well we compare the signal-to-noise ratio resulting from numerical simulations with some quasi-analytical results predicted by a consistent Markovian approximation in the case of a colored non-Gaussian noise. We also study the FitzHugh–Nagumo excitable system in the presence of the same noise.

Physica A: Statistical Mechanics and its Applications, 2013

The stochastic resonance (SR) in bistable systems has been extensively discussed with the use of phenomenological Langevin models. By using the microscopic, generalized Caldeira-Leggett (CL) model, we study in this paper, SR of an open bistable system coupled to a bath with a nonlinear system-bath interaction. The adopted CL model yields the non-Markovian Langevin equation with nonlinear dissipation and state-dependent diffusion which preserve the fluctuationdissipation relation (FDR). From numerical calculations, we find the following: (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 (b) denotes the magnitude of multiplicative (additive) noise and τ expresses the relaxation time of 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. These results (1) and (2) are qualitatively different from previous ones obtained by phenomenological Langevin models where the FDR is indefinite or not held.

Physics Letters A, 2006

We carry out a detailed numerical investigation of stochastic resonance in underdamped systems in the non-perturbative regime. We point out that an important distinction between stochastic resonance in overdamped and underdamped systems lies in the lack of dependence of the amplitude of the noise-averaged trajectory on the noise strength, in the latter case. We provide qualitative explanations for the observed behavior and show that signatures such as the initial decay and long-time oscillatory behaviour of the temporal correlation function and peaks in the noise and phase averaged power spectral density, clearly indicate the manifestation of resonant behaviour in noisy, underdamped bistable systems in the weak to moderate noise regime.

Physical Review E, 2004

Two methods of realizing aperiodic stochastic resonance (ASR) by adding noise and tuning system parameters in a bistable system, after a scale transformation, can be compared in a real parameter space. In this space, the resonance point of ASR via adding noise denotes the extremum of a line segment, whereas the method of tuning system parameters presents the extrema of a parameter plane. We demonstrate that, in terms of the system performance, the method of tuning system parameters takes the precedence of the approach of adding noise for an adjustable bistable system. Besides, adding noise can be viewed as a specific case of tuning system parameters. Further research shows that the optimal system found by tuning system parameters may be subthreshold or suprathreshold, and the conventional ASR effects might not occur in some suprathreshold optimal systems.

Nonlinear Dynamics

In a bistable system excited by the combination of a weak low-frequency signal and a noise, the noise can induce a resonance at the subharmonic frequency which is smaller than the driving frequency. This kind of noise-induced resonance is similar to the well-known stochastic resonance. Here, we verify the noise-induced resonance at the subharmonic frequency which equals 1/3 multiple of the driving frequency, by a numerical study of the response of the overdamped

Physical Review Letters, 2003

An amenable, analytical two-state description of the nonlinear population dynamics of a noisy bistable system driven by a rectangular subthreshold signal is put forward. Explicit expressions for the driven population dynamics, the correlation function (its coherent and incoherent part), the signal-to-noise ratio (SNR) and the Stochastic Resonance (SR) gain are obtained. Within a suitably chosen range of parameter values this reduced description yields anomalous SR-gains exceeding unity and, simultaneously, gives rise to a non-monotonic behavior of the SNR vs. the noise strength. The analytical results agree well with those obtained from numerical solutions of the Langevin equation.

Chaos Solitons & Fractals, 2002

A thorough evaluation of stochastic resonance with tuning system parameters in bistable systems is presented as a nonlinear signal processor. It is shown that the output signal-to-noise ratio obtained by adjusting systems parameters can exceed that by tuning noise intensity, especially when the input noise intensity is already beyond the resonance region. It is demonstrated that the theory and the method presented here can markedly improve the output signal-to-noise ratio, and minimize phase lag as well as the distortion of the system output signal with multi-frequency. Ó

Chinese Physics, 2005

Physica D: Nonlinear Phenomena, 2003

An array of overdamped bistable oscillators with delay was studied numerically. Each site of the array is coupled directionally with the addition of white Gaussian noise. On the other hand, we compared the results with an array of coupled chain of experimental devices, also fed with Gaussian white noise. We observed for an optimal amount of noise and moderated coupling good transmission along the line without degradation.

Circuits and Systems …, 1999

Stochastic resonance (SR), a phenomenon in which a periodic signal in a nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described in practical terms. The physical nature of SR, and the explanation of weak-noise SR as a linear response phenomenon, are considered. Conventional SR, for systems characterized by static bistable potentials, is described together with examples of the data obtainable from the circuit models used to test the theory.