Stochastic resonance in multi-stable system driven by Lévy noise

2018 ◽  
Vol 56 (4) ◽  
pp. 1559-1569 ◽  
Author(s):  
Dongying Han ◽  
Xiao Su ◽  
Peiming Shi
Keyword(s):  
Stochastic Resonance ◽  
Stable System ◽  
Lévy Noise ◽  
Levy Noise

Lévy noise-induced inverse stochastic resonance on Newman–Watts networks of Hodgkin–Huxley neurons

2020 ◽  
Vol 34 (19) ◽  
pp. 2050185
Author(s):  
Dongxi Li ◽  
Shuling Song ◽  
Ni Zhang
Keyword(s):  
Firing Rate ◽  
Stochastic Resonance ◽  
Neuronal Network ◽  
Coupling Strength ◽  
Stability Index ◽  
Neuronal Firing ◽  
Lévy Noise ◽  
Neuron Network ◽  
Average Firing Rate ◽  
Levy Noise

This paper primarily investigates the inverse stochastic resonance (ISR) of neuron network driven by Lévy noise with electrical autapse and chemical autapse, respectively. Firstly, the discharge of Hodgkin–Huxley (HH) neuron network under different noise parameters, autapse parameters and network coupling strength is shown. Then, the variation of average firing rate with Lévy noise in the case of electrical autapse and chemical autapse is presented. We find that there exists a minimum value of the average firing rate curve caused by stability index and noise intensity of Lévy noise across the whole network, which is the phenomenon of ISR. With the increase of autaptic intensity and coupling strength, the ISR inhibitory effect of neuron discharge is weakened. In addition, with the increase of coupling strength, the neuron discharge of neural network is more intense and regular. As a consequence, our work suggests that autaptic intensity and coupling efficient of neuronal network can regulate the neuronal firing activities and suppress the effect of ISR, and Lévy noise can induce ISR phenomenon in Newman–Watts neuronal network.

Effects of Lévy noise in aperiodic stochastic resonance

2007 ◽  
Vol 40 (26) ◽  
pp. 7175-7185 ◽  
Author(s):  
Lingzao Zeng ◽  
Ronghao Bao ◽  
Bohou Xu
Keyword(s):  
Stochastic Resonance ◽  
Lévy Noise ◽  
Levy Noise

Stochastic resonance induced by Lévy noise in a tumor growth model with periodic treatment

2014 ◽  
Vol 28 (11) ◽  
pp. 1450085 ◽  
Author(s):  
Wei Xu ◽  
Mengli Hao ◽  
Xudong Gu ◽  
Guidong Yang
Keyword(s):  
Tumor Growth ◽  
Stochastic Resonance ◽  
Growth Model ◽  
Tumor Therapy ◽  
Stability Index ◽  
Resonance Phenomenon ◽  
Lévy Noise ◽  
Tumor Growth Model ◽  
Periodic Treatment ◽  
Levy Noise

In this paper, the stochastic resonance phenomenon in a tumor growth model under subthreshold periodic therapy and Lévy noise excitation is investigated. The possible reoccurrence of tumor due to stochastic resonance is discussed. The signal-to-noise ratio (SNR) is calculated numerically to measure the stochastic resonance. It is found that smaller stability index is better for avoiding tumor reappearance. Besides, the effect of the skewness parameter on the tumor regrowth is related to the stability index. Furthermore, increasing the intensity of periodic treatment does not always facilitate tumor therapy. These results are beneficial to the optimization of periodic tumor therapy.

Levy noise-induced inverse stochastic resonance in a single neuron

2019 ◽  
Vol 33 (21) ◽  
pp. 1950252
Author(s):  
Yue Zhao ◽  
Dongxi Li
Keyword(s):  
Stochastic Resonance ◽  
Single Neuron ◽  
Scale Parameter ◽  
Stability Index ◽  
Current Strength ◽  
Lévy Noise ◽  
Critical Threshold ◽  
Interspike Intervals ◽  
Discharge Patterns ◽  
Levy Noise

In this paper, the phenomenon of inverse stochastic resonance (ISR) induced by Levy noise is investigated in a single neuron. Firstly, the discharge of Hodgkin–Huxley neuron at different current strengths without noise is studied. Then we cite the concept of average spiking rate and use it as a scale to measure the discharge of neuron. Under the influence of Levy noise, it is found that the average firing rate can reach a minimum caused by stability index and a scale parameter of Levy noise. The conclusion is that ISR could be induced by Levy noise when the input current strength reaches the critical threshold. Besides, in order to further prove that Levy noise can produce ISR, interspike intervals (ISIs) histogram is used for studying discharge patterns in voltage. Finally, we find that with the increase of stability index and scale parameter of Levy noise, the total number of ISIs decreases first and then increases, which implies the appearance of ISR.

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