STOCHASTIC RESONANCE IN A TIME-DELAYED BISTABLE SYSTEM WITH COLORED COUPLING BETWEEN NOISE TERMS

2012 ◽  
Vol 26 (30) ◽  
pp. 1250149 ◽  
Author(s):  
XIAOQIN LUO ◽  
DAN WU ◽  
SHIQUN ZHU
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Coupling Strength ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Bistable System ◽  
Initial Condition

The phenomenon of stochastic resonance (SR) in a time-delayed bistable system with colored coupling between multiplicative and additive noise terms is investigated. The SR can be induced by the multiplicative noise, the time delay and the coupling strength between noise terms. Meanwhile, the SR is affected by the initial condition of the system.

Stochastic resonance in asymmetric time-delayed bistable system under multiplicative and additive noise and its applications in bearing fault detection

2019 ◽  
Vol 33 (28) ◽  
pp. 1950341 ◽  
Author(s):  
Lifang He ◽  
Dayun Hu ◽  
Gang Zhang ◽  
Siliang Lu
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
Random Force ◽  
Small Time ◽  
Delayed Feedback ◽  
Bistable System ◽  
Bearing Fault ◽  
Strength Formula ◽  
Time Delayed Feedback

The asymmetric bistable system with time delays in the feedback force and random force under multiplicative and additive Gaussian noise is studied. Using the small time delay approximation approach and time-delayed Fokker–Planck equations (FPE), the signal-to-noise ratio (SNR) of the proposed stochastic system is obtained. The stochastic resonance (SR) phenomena influenced by parameters — including system parameters [Formula: see text], [Formula: see text], asymmetry parameter [Formula: see text], time delay [Formula: see text], strength [Formula: see text] of the time-delayed feedback, noise intensities [Formula: see text] and [Formula: see text] of multiplicative and additive noise, and correlation strength [Formula: see text] between two noises, are also analyzed by numerical simulations. Results demonstrate that the SR performance of the asymmetric bistable system is superior to one symmetric bistable system. Besides, both time delay and strength of time-delayed feedback could enhance the SR to some extent. Then, the asymmetric time-delayed bistable SR (ATDBSR) method is used to the bearing fault diagnosis. The engineering applications of the ATDBSR method are realized and the value of the method is verified by effective experimental results.

Impact of Time Delay and Cross-Correlated Gaussian Colored Noises on Dynamical Characteristics and Stochastic Resonance for a Metapopulation System

2020 ◽  
pp. 2150024
Author(s):  
Kang-Kang Wang ◽  
De-Cai Zong ◽  
Ya-Jun Wang ◽  
Sheng-Hong Li
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Resonant Peak ◽  
Noise Correlation ◽  
Ecological Stability ◽  
Correlation Times ◽  
Correlation Strength

In this paper, the regime shift behaviors between the prosperous state and the extinction state and stochastic resonance (SR) phenomenon for a metapopulation system subjected to time delay and correlated Gaussian colored noises are investigated. Through the numerical calculation of the modified potential function and the stationary probability density function (SPDF), one can make clearly the following results: Both multiplicative noise and noise correlation times can improve effectively the ecological stability and prolong the survival time of the system; while additive noise, time delay and noise correlation strength can weaken significantly the biological stability and speed up the extinction of the population. As for the signal-to-noise ratio (SNR), it is found that time delay, multiplicative noise and noise correlation strength can all impair the SR effect. Conversely, the two noise correlation times and additive noise are in favor of the improvement of the peak values of SNR. It is particularly worth mentioning that in the case of [Formula: see text], time delay [Formula: see text] and self-correlation time [Formula: see text] of the additive noise display exactly the opposite effect on the stimulation of the resonant peak in the SNR–[Formula: see text] plots.

ASYMMETRIC EFFECTS ON STOCHASTIC RESONANCE IN THE BISTABLE SYSTEM SUBJECT TO CORRELATED NOISES

2012 ◽  
Vol 26 (24) ◽  
pp. 1250125 ◽  
Author(s):  
FEI LONG ◽  
DONGCHENG MEI
Keyword(s):  
Stochastic Resonance ◽  
Multiplicative Noise ◽  
Initial Conditions ◽  
Signal To Noise Ratio ◽  
Bistable System ◽  
Periodic Signal ◽  
Initial Condition ◽  
Asymmetric Effects ◽  
Periodic Signals ◽  
Correlated Noises

Asymmetric effects on the stochastic resonance (SR) in the bistable system with correlated noises are investigated. Based on the theory of signal-to-noise ratio (SNR), the expressions of SNR are derived for the case of the additive signal and the case of the multiplicative signal, respectively. Through the numerical computation, it is found in both cases of additive and multiplicative periodic signals (i) The asymmetric effects on SR phenomenon in the system induced by the multiplicative noise is dependent of initial conditions, i.e., the asymmetric parameter r weakens the SR for the initial condition of x(t = 0) = x+, however, r enhances the SR for the initial condition of x(t = 0) = x-; (ii) The asymmetric effects on SR phenomenon in the system induced by the additive noise and the correlation between noises is independent of initial conditions, i.e., the r always enhance the SR; (iii) Synergistic action of the noises, the correlation between noises, the periodic signal and the system's asymmetry induces symmetry revival.

Stochastic Resonance in FitzHugh-Nagumo Neural Model

2013 ◽  
Vol 415 ◽  
pp. 298-302
Author(s):  
Deng Rong Zhou ◽  
Jian Chun Gong ◽  
Dan Li
Keyword(s):  
Stochastic Resonance ◽  
Adiabatic Approximation ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Neural Model ◽  
System Parameters ◽  
Maximum Value ◽  
External Incentives ◽  
Delayed Time

Stochastic resonance is a non-linear phenomenon where the output response of the dynamic system reaches the maximum value under the joint action of a certain intensity of noises and external incentives. In this paper, the phenomenon of stochastic resonance in a FitzHugh-Nagumo neural (FHN) model is studied. For the case that the frequency of the HF signal is much higher than that of the LF signal, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) with respect to the LF signal is obtained. It is shown that, the SNR is a non-monotonous function of the amplitude and frequency of the HF signal. In addition, the SNR varies non-monotonically with increasing the intensities of the multiplicative and additive noise, with increasing the delayed-time as well as increasing the system parameters of the FHN model. The influence of the correlation time of the colored multiplicative noise and the influence of the coupling strength between the multiplicative and additive noise on the SNR is discussed.

SIMULATION STUDY OF NOISE-ENHANCED STABILITY AND RESONANT ACTIVATION IN A BISTABLE SYSTEM INDUCED BY TIME DELAY

2011 ◽  
Vol 25 (02) ◽  
pp. 141-149 ◽  
Author(s):  
CHUN LI ◽  
LUCHUN DU ◽  
DONGCHENG MEI
Keyword(s):  
Time Delay ◽  
Thermal Activation ◽  
Multiplicative Noise ◽  
Bistable System ◽  
Peak Structure ◽  
Activation Rate ◽  
Linear Delay ◽  
Resonant Activation ◽  
Correlated Noises ◽  
Enhanced Stability

The thermal activation problem of a bistable system driven by correlated noises with time delay is investigated by means of numerical simulations. The simulation results indicate: (1) For the case of the bistable system with linear delay, the phenomenon of noise enhanced stability (NES) is enforced by increasing delay time τ as the multiplicative noise intensity D is smaller, but is weakened as D is larger. (2) For the case of the bistable system with cubic delay, the NES becomes faintness as τ increases. (3) For the case of the bistable system with global delay, the NES is still restrained by increasing τ with smaller D, and in some circumstances, the activation rate as a function of τ exists a peak structure, which demonstrating the emergence of resonant activation.

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