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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]