Stochastic resonance driven by Gaussian multiplicative noise

1997 ◽  
Vol 40 (2) ◽  
pp. 117-122 ◽  
Author(s):  
A. V Barzykin ◽  
K Seki
Keyword(s):  
Stochastic Resonance ◽  
Multiplicative Noise

Stochastic resonance and stability for an ecological vegetation growth system driven by colored noises and multiplicative signal

2016 ◽  
Vol 30 (24) ◽  
pp. 1650308 ◽  
Author(s):  
Kang-Kang Wang ◽  
Ya-Jun Wang ◽  
Jian-Cheng Wu
Keyword(s):  
Stochastic Resonance ◽  
Multiplicative Noise ◽  
Signal To Noise Ratio ◽  
Periodic Signal ◽  
Expansion Process ◽  
Correlation Times ◽  
Vegetation Growth ◽  
Growth System ◽  
Speed Up ◽  
The Stability

In this paper, we investigate the steady-state properties and the transition rate for an ecological vegetation growth system induced by the terms of the colored multiplicative and additive noises. Numerical results indicate that the multiplicative noise and the additive one can reduce the stability of the ecological system and slow down the development velocity of the vegetation, while two noise self-correlation times can increase the stability of the system and speed up the expansion process of the vegetation system. With respect to the stochastic resonance (SR) phenomenon caused by noise terms and a multiplicative weak periodic signal, the results show that the additive noise always enhances the SR effect, two noise self-correlation time terms can produce SR phenomenon, but play opposite roles in enhancing or inhibiting the SR effect under different parameter conditions. In particular, the two self-correlation times can keep up the maximum of the signal-to-noise ratio (SNR) invariant in specific situations. Analogously, the multiplicative noise can not only improve the SNR, but also restrain the SR phenomenon in different cases.

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.

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.

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 FOR A METAPOPULATION SYSTEM SUBJECTED TO CORRELATED COLORED NOISES

2013 ◽  
Vol 27 (18) ◽  
pp. 1350136 ◽  
Author(s):  
KANG-KANG WANG ◽  
XIAN-BIN LIU ◽  
SHENG-HONG LI
Keyword(s):  
Stochastic Resonance ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Signal To Noise Ratio ◽  
State Theory ◽  
Descent Method ◽  
Correlated Noise ◽  
Signal To Noise ◽  
System Parameters ◽  
Fast Descent

In the present paper, for a Levins metapopulation system that is driven by correlated colored noises, the phenomenon of stochastic resonance (SR) is investigated. Based on the two-state theory and by the use of fast descent method, the expression of the signal-to-noise ratio (SNR) is obtained. Via a numerical simulation, it is shown that the conventional SR occurs in the Levins model for the different values of system parameters. And furthermore, it is revealed that, under the different conditions that if the correlation intensities between the two noises are different, i.e. positive or negative, then all the effects of the addictive noise intensity, the multiplicative noise intensity, the correlated noise intensity and the correlation time on SNR are different.

Stochastic resonance with multiplicative noise in a three-level atomic bistable system

2007 ◽  
Vol 54 (16-17) ◽  
pp. 2441-2450 ◽  
Author(s):  
Haibin Wu ◽  
Amitabh Joshi ◽  
Min Xiao
Keyword(s):  
Stochastic Resonance ◽  
Multiplicative Noise ◽  
Bistable System
Sign in / Sign up

Export Citation Format

Share Document