Impact of Time Delay and Non-Gaussian Noise on Stochastic Resonance and Stability for a Stochastic Metapopulation System Driven by a Multiplicative Periodic Signal

2019 ◽  
Vol 18 (03) ◽  
pp. 1950017
Author(s):  
Kang-Kang Wang ◽  
Hui Ye ◽  
Ya-Jun Wang ◽  
Ping-Xin Wang
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Gaussian Noise ◽  
Correlation Time ◽  
Multiplicative Noise ◽  
Periodic Signal ◽  
Population System ◽  
The Stability ◽  
Non Gaussian ◽  
Multiplicative Periodic Signal

In the present paper, the stability of the population system and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by the terms of time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal are investigated in detail. By applying the fast descent method, the unified colored noise approximation and the SR theory, the expressions of the steady-state probability function and the SNR are derived. It is shown that multiplicative non-Gaussian noise, the additive Gaussian noise and time delay can all weaken the stability of the population system, and even result in population extinction. Conversely, the two noise correlation times can both strengthen the stability of the biological system and contribute to group survival. In regard to the SNR for the metapopulation system impacted by the noise terms and time delay, it is revealed that the correlation time of the multiplicative noise can improve effectively the SR effect, while time delay would all along restrain the SR phenomena. On the other hand, although the additive noise and its correlation time can stimulate easily the SR effect, they cannot change the maximum of the SNR. In addition, the departure parameter from the Gaussian noise and the multiplicative noise play the opposite roles in motivating the SR effect in different cases.

Time delay and non-Gaussian noise-induced stochastic stability and stochastic resonance for a metapopulation system subjected to a multiplicative periodic signal

2018 ◽  
Vol 32 (27) ◽  
pp. 1850327 ◽  
Author(s):  
Kang-Kang Wang ◽  
Hui Ye ◽  
Ya-Jun Wang ◽  
Ping-Xin Wang
Keyword(s):  
Time Delay ◽  
Gaussian Noise ◽  
Correlation Time ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Periodic Signal ◽  
Colored Gaussian Noise ◽  
The Stability ◽  
Non Gaussian ◽  
Multiplicative Periodic Signal

In this paper, the stable state transformation and the effect of the stochastic resonance (SR) for a metapopulation system are investigated, which is disturbed by time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal. By use of the fast descent method, the approximation of the unified colored noise and the SR theory, the dynamical behaviors for the steady-state probability function and the SNR are analyzed. It is found that non-Gaussian noise, the colored Gaussian noise and time delay can all reduce the stability of the biological system, and even lead to the population extinction. Inversely, the self-correlation times of two noises can both increase the stability of the population system and be in favor of the population reproduction. As regards the SNR for the metapopulation system induced by the noise terms and time delay, it is discovered that time delay and the correlation time of the multiplicative noise can effectively enhance the SR effect, while the multiplicative noise and the correlation time of the additive noise would all the time suppress the SR phenomena. In addition, the additive noise can effectively motivate the SR effect, but not alter the peak value of the SNR. It is worth noting that the departure parameter from the Gaussian noise plays the diametrical roles in stimulating the SR effect in different cases.

Stochastic Kinetics for a FitzHugh–Nagumo Neural System with Time Delay Driven by Non-Gaussian Noise and a Multiplicative Periodic Signal

2019 ◽  
Vol 18 (04) ◽  
pp. 1950027 ◽  
Author(s):  
Kang-Kang Wang ◽  
De-Cai Zong ◽  
Hui Ye ◽  
Ya-Jun Wang
Keyword(s):  
Time Delay ◽  
Probability Density ◽  
Gaussian Noise ◽  
Correlation Time ◽  
Neural System ◽  
Noise Correlation ◽  
Stable States ◽  
The Stability ◽  
Non Gaussian ◽  
System With Time Delay

In the present paper, the stability and the phenomena of stochastic resonance (SR) for a FitzHugh–Nagumo (FHN) system with time delay driven by a multiplicative non-Gaussian noise and an additive Gaussian white noise are investigated. By using the fast descent method, unified colored noise approximation and the two-state theory for the SR, the expressions for the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) are obtained. The research results show that the two noise intensities and time delay can always decrease the probability density at the two stable states and impair the stability of the neural system; while the noise correlation time [Formula: see text] can increase the probability density around both stable states and consolidate the stability of the neural system. Furthermore, the other noise correlation time [Formula: see text] can increase the probability at the resting state, but reduce that around the excited state. With respect to the SNR, it is discovered that the two noise strengths can both weaken the SR effect, while time delay [Formula: see text] and the departure parameter [Formula: see text] will always amplify the SR phenomenon. Moreover, the noise correlation time [Formula: see text] can motivate the SR effect, but not alter the peak value of the SNR. What’s most interesting is that the other noise correlation time [Formula: see text] can not only stimulate the SR phenomenon, but also results in the occurrence of two resonant peaks, whose heights are simultaneously improved because of the action of [Formula: see text].

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.

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