Non-Gaussian noise induced stochastic resonance in FitzHugh–Nagumo neural 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].

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Stochastic resonance in FHN neural system driven by non-Gaussian noise

Acta Physica Sinica ◽

10.7498/aps.61.130502 ◽

2012 ◽

Vol 61 (13) ◽

pp. 130502

Author(s):

Zhang Jing-Jing ◽

Jin Yan-Fei

Keyword(s):

Stochastic Resonance ◽

Gaussian Noise ◽

Neural System ◽

Non Gaussian

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Non-Gaussian noise-weakened stability in a foraging colony system with time delay

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2017.11.015 ◽

2018 ◽

Vol 492 ◽

pp. 851-870 ◽

Cited By ~ 14

Author(s):

Xiaohui Dong ◽

Chunhua Zeng ◽

Fengzao Yang ◽

Lin Guan ◽

Qingshuang Xie ◽

...

Keyword(s):

Time Delay ◽

Gaussian Noise ◽

Non Gaussian ◽

System With Time Delay

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

Fluctuation and Noise Letters ◽

10.1142/s0219477519500172 ◽

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.

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Stochastic resonance in FitzHugh–Nagumo neural system driven by correlated non-Gaussian noise and Gaussian noise

International Journal of Modern Physics B ◽

10.1142/s0217979217502642 ◽

2017 ◽

Vol 31 (32) ◽

pp. 1750264 ◽

Cited By ~ 5

Author(s):

Yong-Feng Guo ◽

Bei Xi ◽

Fang Wei ◽

Jian-Guo Tan

Keyword(s):

Stochastic Resonance ◽

Gaussian Noise ◽

Noise Intensity ◽

Signal To Noise Ratio ◽

Gaussian White Noise ◽

Neural System ◽

Integral Approach ◽

Stationary Probability Distribution ◽

Non Gaussian ◽

Two State Model

In this paper, the phenomenon of stochastic resonance in FitzHugh–Nagumo (FHN) neural system driven by correlated non-Gaussian noise and Gaussian white noise is investigated. First, the analytical expression of the stationary probability distribution is derived by using the path integral approach and the unified colored noise approximation. Then, we obtain the expression of signal-to-noise ratio (SNR) by applying the theory of two-state model. The results show that the phenomena of stochastic resonance and multiple stochastic resonance appear in FHN neural system under different values of parameters. The effects of the multiplicative noise intensity D and the additive noise intensity Q on the SNR are entirely different. In addition, the discharge behavior of FHN neural system is restrained when the value of Q is smaller. But, it is conducive to enhance signal response of FHN neural system when the values of Q and D are relatively larger.

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Dynamical behavior of simplified FitzHugh–Nagumo neural system with time delay driven by Lévy noise

International Journal of Modern Physics B ◽

10.1142/s0217979221502404 ◽

2021 ◽

pp. 2150240

Author(s):

Weida Qiu ◽

Yongfeng Guo ◽

Xiuxian Yu

Keyword(s):

Time Delay ◽

First Passage Time ◽

Dynamical Behavior ◽

Passage Time ◽

Neural System ◽

The Other ◽

Lévy Noise ◽

First Passage ◽

Levy Noise ◽

System With Time Delay

In this paper, the dynamical behavior of the FitzHugh–Nagumo (FHN) neural system with time delay driven by Lévy noise is studied from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using the Janicki–Weron algorithm to generate the Lévy noise, and through the order-4 Runge–Kutta algorithm to simulate the FHN system response, the time that the system needs from one stable state to the other one is tracked in the process. Using the MATLAB software to simulate the process above 20,000 times and recording the PFTs, the PDF of the FPT and the MFPT is obtained. Finally, the effects of the Lévy noise and time-delay on the FPT are discussed. It is found that the increase of both time-delay feedback intensity and Lévy noise intensity can promote the transition of the particle from the resting state to the excited state. However, the two parameters produce the opposite effects in the other direction.

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