《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (9): 1-9.

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### 电磁感应下HR神经元模型的分岔分析与控制

1. 兰州交通大学数理学院, 甘肃 兰州 730070
• 发布日期:2020-09-17
• 作者简介:乔帅(1995— ),男,硕士研究生,研究方向为非线性动力学. E-mail:1653826027@qq.com*通信作者简介:安新磊(1983— ),男,博士,副教授,研究方向为非线性动力学. E-mail:anxin1983@163.com
• 基金资助:
国家自然科学基金资助项目(61863022);甘肃省自然科学基金资助项目(17JR5RA096);兰州交通大学研究生教育改革项目(JG201816)

### Bifurcation analysis and control of HR neuron model under electromagnetic induction

QIAO Shuai, AN Xin-lei*, WANG Hong-mei, ZHANG Wei

1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
• Published:2020-09-17

Abstract: It is of great value to study the firing activity of neurons under electromagnetic radiation for the control and treatment of neuron-related lesions. Based on the theoretical analysis and numerical simulation, the bifurcation structure of HR neuron model of magnetic flux and its stability control of subcritical Hopf bifurcation are studied. Through the numerical simulation, it is found that the system has alternations of plus period 1 bifurcation, double period bifurcation and chaos in the two-parameter region. In addition, through the theoretical analysis of distribution and stability of the system equilibrium point under the change of external stimulus current, it is concluded that there exists a supercritical Hopf bifurcation point in the system, and a hidden limit cycle attractor is found near the subcritical Hopf bifurcation point. By using Washout controller, the subcritical Hopf bifurcation stability control is realized, which eliminates the phenomenon of hidden discharge and helps reveal and understand the internal mechanism of the generation and transformation of hidden discharge in neurons.

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