Stochastic resonance, reverse-resonance, and resonant activation induced by a multi-state noise

In this paper, we investigate the periodic response for a linear system driven by a multiplicative multi-state noise (which is composed of the multiplication of two dichotomous noises) to an input temporal oscillatory signal, and the escape of Brownian particles over the fluctuating potential barrier for a system with a piece-wise linear potential and driven by an additive multi-state noise (which is also composed of the multiplication of two dichotomous noises). For the first system, we get the stochastic resonance phenomenon for the amplitude of the periodic response vs. the two dichotomous noise strengths, and the phenomenon of reverse-resonance for the amplitude of the periodic response vs. k, which represents the asymmetry degree of the dichotomous noises. For the second system, we obtain the resonant activation phenomenon, for which the mean first passage time of the Brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi-state noise.     

Effect of Correlated Dichotomous Noises on Stochastic Resonance in a Linear System

A linear system driven by correlated asymmetric dichotomous noises and periodic signal was investigated in the overdamped case. The exact expressions of output signal amplitude and signal-to-noise ratio (SNR) of the system were derived. By means of numerical calculations, we found that: (i) At some fixed multiplicative noise intensities, the output signal amplitude with frequency exhibits the structure of a weak peak, even no peak as the dichotomous noise is asymmetric; (ii) In the case of asymmetric dichotomous noise, the signal frequency can cause non-monotonous behavior of the output signal amplitude with respect to multiplicative noise intensity; (iii) The curve of SNR with frequency has a weak peak and a trough in the case of symmetric dichotomous noise, but no peak with asymmetric; (iv) Whether the multiplicative noise is symmetric or asymmetric, the noise can enhance response of the system; (v) The SNR increases with the correlation strength between the two noises decreasing. In addition, the plane of multiplicative noise intensity versus noise symmetric parameter was plotted.     

Stochastic resonance in linear system driven by multiplicative noise and additive quadratic noise

In this paper the stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative noise and additive quadratic noise. The exact expressions are obtained for the first two moments and the correlation function by using linear response and the properties of the dichotomous noise. SR phenomenon exhibits in the linear system. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the effect of the asymmetry of the multiplicative noise on the signal-to-noise ratio (SNR) is different from that of the additive noise and the effect of multiplicative noise and additive noise on SNR is different.     

Resonance behavior for an underdamped bistable system driven by square-wave signal and multiplicative noise

The stochastic resonance (SR) behavior for an underdamped bistable system driven by square-wave signal and multiplicative noise is investigated. Under the adiabatic approximation condition, the expression for the system output signal-to-noise ratio (SNR) is obtained. The analysis results show that stochastic multi-resonance phenomenon occurs when the SNR varies with the intensities of the multiplicative and additive noise. SR phenomenon can be observed on the curves of the SNR versus the system bias, versus the amplitude of the dichotomous noise and versus the amplitude of the square-wave signal. Moreover, the SNR varies non-monotonously with the variety of other system parameters.     

Effect of Asymmetry in a Bistable System Subject to Multiplicative Colored Noise

By the method of the stochastic energetics, we investigate the stochastic resonance (SR) phenomenon of an overdamped Brown particle in an asymmetric bistable potential, driven by external periodical signal and multiplicative noise. The expressions have been obtained for the quasi-steady-state probability distribution function. It is found that the input energy (IE) pumped into the system by the external driving shows an SR-like behavior as a function of the noise strength, whereas the IE turns to be a monotonic function of the correlation time of the noise. The effect of potential asymmetry is also studied on SR and IE.     

Stochastic resonance in linear system driven by multiplicative and additive noise

The stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative and additive noise when the additive noise is a linear combination of an asymmetric dichotomous noise and its square. The exact expressions are obtained for the first two moments and the correlation function and the SR phenomenon appeared. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the asymmetry of multiplicative noise has different effect on signal-to-ratio (SNR) for the first two different forms of SR and the effects of multiplicative noise and additive noise on SNR are different.     

Stochastic resonance in a time-delayed bistable system subject to multiplicative and additive noise

This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise.Under the adiabatic approximation condition,the expression of the signal-to-noise ratio (SNR) is obtained.It finds that the SNR is a non-monotonic function of the delayed times,of the amplitude of the driving square-wave signal,as well as of the asymmetry of the dichotomous noise.In addition,the SNR varies non-monotonously with the intensities of the multiplicative and additive noise as well as the system parameters.Moreover,the SNR depends non-monotonically on the correlate rate of the dichotomous noise.     

Giant-Resonance for a Four-Dimensionally Coupled System with Dichotomous Noise

In this paper, we investigate a four-dimensionally coupled system driven by dichotomous noise. A new kind of stochastic resonance is found, for which the response of the system to the input signal can be hugely intensified.     

Two Stochastic Resonances Induced by Two Different Multiplicative Telegraphic Noises for an Electric System

In this paper, an electric system with two dichotomous resistors is investigated. It is shown that this system can display two stochastic resonances, which are the amplitude of the periodic response as the functions of the two dichotomous resistors strengthes respectively. In the limits of Gaussian white noise and shot white noise (i.e., the two noises are both Gaussian white noise or shot white noise), no phenomena of resonance appear. By further study, we find that when the system is with three or more multiplicative telegraphic noises, there are three or more stochastic resonances.     

二值噪声激励下欠阻尼周期势系统的随机共振

研究了二值噪声和周期信号共同激励下欠阻尼周期势系统的随机共振. 利用随机能量法计算了系统的平均输入能量和平均输出信号的振幅和相位差, 讨论了二值噪声对随机共振的影响. 发现随着噪声强度的增大, 平均输入能量曲线存在一个极小值和一个极大值, 系统出现先抑制后共振的现象; 同时, 系统信噪比曲线随噪声强度的增加出现单峰现象, 说明系统存在随机共振现象.     

Hypersensitivity to small signals in a stochastic system with multiplicative colored noise

Recently we discovered the phenomenon of hypersensitivity to small time-dependent signals in a simple stochastic system, the Kramers oscillator with multiplicative white noise. In the present work we study, theoretically and experimentally with analog simulations, an influence of noise correlation time on hypersensitivity in a nonlinear oscillator with piecewise-linear current-voltage characteristic and multiplicative colored dichotomous noise. We found that the region of hypersensitive behavior is defined by universal scaling index, whereas the specifics of a particular system reveals itself only in the dependence of the above index on system parameters. The dependence of gain factor on noise correlation time is of bell-shaped (resonant) type. Received 27 April 2000 and Received in final form 2 November 2000     

Stochastic multi-resonance in an overdamped bistable system with two types of modulation signal

The stochastic resonance (SR) phenomenon in an overdamped bistable system with multiplicative and additive noise is investigated. The signal-to-noise ratio (SNR) is calculated when two types of modulation signal are added to the system. The effects of the intensities, the frequencies and relative phase shift of two types of modulation signal on the SNR are discussed, respectively. Research results show that: (i) the intensities of two types of modulation signal can enhance the maximum in the SNR as a function of the noise intensity, and the frequencies can restrain it; (ii) the additive modulation signal can enhance the maximum in the SNR as a function of the noise intensity in comparison with the multiplicative modulation signal; (iii) when both modulation frequencies are equal, the SNR as a function of the relative phase shift exhibits multiple maxima. The multiple maxima in the SNR identifies the characteristic of the stochastic multi-resonance phenomenon.     

Stochastic resonance in a bias linear system with multiplicative and additive noise

In this paper, the stochastic resonance in a bias linear system subjected multiplicative and additive dichotomous noise is investigated. Using the linear-response theory and the properties of the dichotomous noise, this paper finds the exact expressions for the first two moments and the signal-to-noise ratio (SNR). It is shown that the SNR is a non-monotonic function of the correlation time of the multiplicative and additive noise, and it varies non-monotonously with the intensity and asymmetry of the multiplicative noise as well as the external field frequency. Moreover, the SNR depends on the system bias, the intensity of the cross noise between the multiplicative and additive noise, and the strength and asymmetry of the additive noise.     

光学双稳系统中的随机共振

运用绝热近似理论，研究了由加性噪声和乘性噪声及周期信号驱动的光学双稳系统的随机共振现象. 发现该模型中输出信噪比R～随着加性噪声强度D_a的变化曲线中会出现随机共振现象，而信噪比R～随着乘性噪声强度D_m的变化曲线是单调减小的，信噪比曲线中没有出现随机共振现象. 因此，加性噪声和乘性噪声对输出信噪比的影响是不同的. 关键词： 随机共振 信噪比 乘性噪声 加性噪声     

Effect of inertial mass on a linear system driven by dichotomous noise and a periodic signal

A linear system driven by dichotomous noise and a periodic signal is investigated in the underdamped case. The exact expressions of output signal amplitude and signal-to-noise ratio (SNR) of the system are derived. By means of numerical calculation, the results indicate that (i) at some fixed noise intensities, the output signal amplitude with inertial mass exhibits the structure of a single peak and single valley, or even two peaks if the dichotomous noise is asymmetric; (ii) in the case of asymmetric dichotomous noise, the inertial mass can cause non-monotonic behaviour of the output signal amplitude with respect to noise intensity; (iii) the curve of SNR versus inertial mass displays a maximum in the case of asymmetric dichotomous noise, i.e., a resonance-like phenomenon, while it decreases monotonically in the case of symmetric dichotomous noise; (iv) if the noise is symmetric, the inertial mass can induce stochastic resonance in the system.     

Noise-controlled slow–fast oscillations in predator–prey models with the Beddington functional response

The influence of environmental fluctuations (modeled as a multiplicative dichotomous noise) on predator–prey interaction is studied using a metapopulation model with N prey-subpopulations. Investigating the role that predator interference plays in the dynamics of such trophic systems, the Beddington functional response is considered. In case the growth rates of prey and predator are widely different, we obtain analytic results by a dynamical mean-field approximation. In some regions of the system parameters, variations of noise amplitude or correlation time can cause transitions of the mean field from a globally stable equilibrium to the stable limit cycle as well as in the opposite direction. The conditions for the occurrence of such a phenomenon are found and illustrated by phase diagrams. Implications of the results on the colored-noise-induced extinction of a predator population are also discussed.     

Enhancement and weakening of stochastic resonance for a coupled system

In the paper, we investigate the phenomenon of stochastic resonance of a system with finite locally coupled linear elements driven by multiplicative dichotomous noise and temporal periodic signal. It is shown that, for some suitably selected values of the parameters, with increasing the size of the system or the coupling among the nearest elements, the stochastic resonance phenomenon can be enhanced; while for some other suitably selected parameters' values, with the increase of the size or the coupling, the phenomenon of stochastic resonance can be weakened. Our results can provide some useful insights for the investigation of the stochastic resonance phenomenon of the systems with locally (or globally) coupled finite (or infinite) elements.     

Modulated stochastic multiresonance in single-mode laser system without input periodic signal

The stochastic resonance phenomenon in a single-mode laser system driven by multiplicative and additive Gaussian white noises without external periodic force is studied. We find that there are multiple extrema (maximum) in the curve of the mean output laser intensity versus the logarithm of multiplicative noise level. This phenomenon reveals that the mean output laser intensity can be amplified at several values of the multiplicative noise intensity, whose peaks are likely modulated by a sinusoidal function.