Stochastic resonance for a forest growth system subjected to non-Gaussian noises and a multiplicative periodic signal

2017 ◽  
Vol 55 (4) ◽  
pp. 1387-1399 ◽  
Author(s):  
Kang-Kang Wang ◽  
Zu-Run Xu ◽  
Ya-Jun Wang ◽  
Sheng-Hong Li
Keyword(s):  
Stochastic Resonance ◽  
Forest Growth ◽  
Periodic Signal ◽  
Growth System ◽  
Non Gaussian ◽  
Multiplicative Periodic Signal

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.

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.

Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Chunyan Bai ◽  
Luchun Du ◽  
Dongcheng Mei
Keyword(s):  
Stochastic Resonance ◽  
Growth Model ◽  
Noise Intensity ◽  
Critical Phenomenon ◽  
Fixed Ratio ◽  
Logistic Growth ◽  
Periodic Signal ◽  
Logistic Growth Model ◽  
Multiplicative Periodic Signal ◽  
Correlated Noises

AbstractThe stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.

Stochastic resonance in a time-delayed tumor cell growth system driven by additive and multiplicative noises

2018 ◽  
Vol 32 (22) ◽  
pp. 1850259 ◽  
Author(s):  
Gang Zhang ◽  
Jiabei Shi ◽  
Tianqi Zhang
Keyword(s):  
Time Delay ◽  
Cell Growth ◽  
Tumor Cell ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
State Theory ◽  
Periodic Signal ◽  
Tumor Cell Growth ◽  
System Parameters ◽  
Growth System

In this paper, the stochastic resonance (SR) phenomenon in a time-delayed tumor cell growth system subjected to a multiplicative periodic signal, the multiplicative and additive noise is investigated. By applying the small time-delay method and two-state theory, the expressions of the mean first-passage time (MFPT) and signal-to-noise ratio (SNR) are obtained, then, the impacts of time delay, noise intensities and system parameters on the MFPT and SNR are discussed. Simulation results show that the multiplicative and additive noise always weaken the SR effect; while time delay plays a key role in motivating the SR phenomenon when noise intensities take a small value, it will restrain SR phenomenon when noise intensities take a large value; the cycle radiation amplitude always plays a positive role in stimulating the SR phenomenon, while, system parameters play different roles in motivating or suppressing SR under the different conditions of noise intensities.

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