JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (9): 1-9.doi: 10.6040/j.issn.1671-9352.0.2019.634


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.

Key words: two-parameter bifurcation analysis, Hopf bifurcation analysis, hidden attractor, Washout controller

CLC Number: 

  • O441
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