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

PDF (PC)

685

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
[1] IZHIKEVICH E M. Dynamical systems in neuroscience: the geometry of excitability and bursting[M]. Boston: Massachusetts Institute of Technology Press, 2007.
[2] HODGKIN A L, HUXLEY A F. The components of membrane conductance in the giant axon of Loligo[J]. The Journal of Physiology, 1952, 116(4):473-496.
[3] MORRIS C, LECAR H. Voltage oscillations in the barnacle giant muscle fiber[J]. Biophysical Journal, 1981, 35(1):193-213.
[4] HINDMARSH J L, ROSE R M. A model of neuronal bursting using three coupled first order differential equations[J]. Proceedings of the Royal Society B: Biological Sciences, 1984, 221(1222):87-102.
[5] LV Mi, WANG Chuni, REN Guodong, et al. Model of electrical activity in a neuron under magnetic flow effect[J]. Nonlinear Dynamics, 2016, 85(3):1479-1490.
[6] 乔帅,张莉,安新磊,等.电磁辐射下HR神经元模型的分岔分析[J].河北师范大学学报(自然科学版),2019,43(4):122-128. QIAO Shuai, ZHANG Li, AN Xinlei, et al. Bifurcation analysis of HR neuron model under electromagnetic radiation[J]. Journal of Hebei Normal University(Natural Science Edition), 2019, 43(4):122-128.
[7] MEGAM N E B, FOTSIN H B, LOUODOP F P, et al. Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator[J]. Chaos, Solitons & Fractals, 2016, 85(6):151-163.
[8] WU Kaijun, LUO Tianqi, LU Huaiwei, et al. Bifurcation study of neuron firing activity of the modified Hindmarsh-Rose model[J]. Neural Computing and Applications, 2016, 27(3):739-747.
[9] 李颖.带有单时滞HR神经元模型的正平衡点稳定性分析[J].甘肃科技纵横,2017,46(1):52-56. LI Ying. Stability analysis of positive equilibrium point with single delay HR neuron model[J]. Gansu Science and Technology, 2017, 46(1):52-56.
[10] 于欢欢,安新磊,路正玉,等.具有时滞磁通神经元模型的Hopf分岔分析[J].吉林大学学报(理学版), 2019,57(5):1111-1121. YU Huanhuan, AN Xinlei, LU Zhengyu, et al. Hopf bifurcation analysis with time-delay magnetic flux neuron model[J]. Journal of Jilin University(Science Edition), 2019, 57(5):1111-1121.
[11] SONG Xinlin, WANG Chuni, MA Jun, et al. Transition of electric activity of neurons induced by chemical and electric autapses[J]. Science China Technological Sciences, 2015, 58(6):1007-1014.
[12] 李佳佳,吴莹,独盟盟,等.电磁辐射诱发神经元放电节律转迁的动力学行为研究[J].物理学报, 2015,64(3):224-230. LI Jiajia, WU Ying, DU Mengmeng, et al. Dynamic behavior of electromagnetic radiation induced neuronal discharge rhythm transfer[J]. Acta Physica Sinica, 2015, 64(3):224-230.
[13] USHA K, SUBHA P A. Hindmarsh-Rose neuron model with memristors[J]. Biosystems, 2019, 303(18):1-17.
[14] 丁真.电磁辐射暴露诱发细胞恶性转化作用机制及电磁防护研究[D].北京:北京工业大学,2017. DING Zhen. Mechanism and electromagnetic protection of malignant transformation induced by electromagnetic radiation exposure[D]. Beijing: Beijing University of Technology, 2017.
[15] 吕密.电磁辐射下神经元的建模及其动力学分析[D].兰州:兰州理工大学,2017. LV Mi. Modeling and dynamic analysis of neurons under electromagnetic radiation[D]. Lanzhou: Lanzhou University of Technology, 2017.
[16] 袁春华.神经元动力学分析与放电特性的研究[D].天津:天津大学,2017. YUAN Chunhua. Dynamic analysis and discharge characteristics of neurons[D]. Tianjin: Tianjin University, 2017.
[17] WANG Xuedi, DENG Lianwang, ZHANG Wenli. Hopf bifurcation analysis and amplitude control of the modified Lorenz system[J]. Applied Mathematics and Computation, 2013, 225(9):333-344.
[18] WANG Haixia, ZHENG Yanhong, LU Qishao. Stability and bifurcation analysis in the coupled HR neurons with delayed synaptic connection[J]. Nonlinear Dynamics, 2017, 88(3):2091-2100.
No related articles found!
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd