Time delay effects of stochastic resonance induced by multiplicative periodic signal in the gene transcriptional regulatory model

2018 ◽  
Vol 507 ◽  
pp. 304-311 ◽  
Author(s):  
Chunyan Bai
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Periodic Signal ◽  
Transcriptional Regulatory ◽  
Delay Effects ◽  
Multiplicative Periodic Signal ◽  
Regulatory Model

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.

Stability and Stochastic Resonance for a Time-Delayed Cancer Development System Subjected to Noises and Multiplicative Periodic Signal

2017 ◽  
Vol 16 (03) ◽  
pp. 1750022 ◽  
Author(s):  
Kang-Kang Wang ◽  
Ya-Jun Wang ◽  
Sheng-Hong Li
Keyword(s):  
Time Delay ◽  
Cancer Cells ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
Critical Role ◽  
State Theory ◽  
Cancer Development ◽  
Periodic Signal ◽  
Development System ◽  
Multiplicative Periodic Signal

In this paper, the stability and the phenomenon of stochastic resonance (SR) for a stochastic time-delayed cancer development system that is induced by the multiplicative periodic signal, the multiplicative and the additive noises are investigated. By using the fast descent method, small time delay method and the two-state theory, the expressions of the steady state probability distribution function and the signal-to-noise ratio (SNR) are obtained. Numerical results reflect that the multiplicative and additive noise always restrain the diffusion of the cancer cells. Whereas, the time delay can not only control the spread of the tumor cells, but also suppress the extinction of cancer cells. Meanwhile, the conventional SR occurs in the tumor cell growth model under the excitation of different noises and time delay. In conclusion, the multiplicative noise always plays a critical role in restraining SR, a smaller additive noise can stimulate the SR, but the larger additive noise can weaken the SR and SNR. In particular, the time delay displays relatively complicated effects on the SR phenomenon of the system. It plays different roles in motivating or suppressing SR under the different conditions of parameters.

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.

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