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Journal of Applied Nonlinear Dynamics 13(4) (2024) 667--682 | DOI:10.5890/JAND.2024.12.005

Yan Liu$^{1}$, Yiming He$^{1}$, He Zhang$^{1}$, Xiaoming Yu$^{2}$, Jianwu Zhou$^{3}$

$^{1}$ School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shanxi, 710072, PR China

$^{2}$ Huaneng Xinjiang Energy Development Co., Ltd. Energy Branch, Urumqi, Xinjiang, 830017, PR China

$^3$ Huaneng Xinjiang Energy Development Co., Ltd., Urumqi, Xinjiang, 830017, PR China

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Abstract

In this paper, the dynamics and synchronization characteristics of a single Hindmarsh-Rose neuron and electrical coupling system have been studied. At first, a method for calculating the eigenvalues of the critical point at the discharge state was applied to analyze the bifurcation of the single Hindmarsh-Rose model. Then, the resting state, periodic firing state, and chaotic state under different excitations are obtained. Furthermore, the relationships between the synchronization state and the coupling strength and time delay are investigated in numerical models. The results show that the time lag could cause waveform attenuation and affect synchronization. Finally, circuit models were proposed to simulate the discharge behaviors of neurons. After comparison, the circuit models reproduce some results with acceptable errors. These results can help understand the firing mechanisms and hardware implementation of neurons.

Acknowledgments

This research is supported by National Natural Science Foundation of China (No.51775437) and State Key Laboratory of Compressor Technology of China(No.SKL-YSJ201902).

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