电磁感应下HR神经元模型的分岔分析与控制  

Bifurcation analysis and control of HR neuron model under electromagnetic induction

作　　者：乔帅 安新磊[1] 王红梅 张薇 QIAO Shuai;AN Xin-lei;WANG Hong-mei;ZHANG Wei(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2020年第9期1-9,共9页Journal of Shandong University(Natural Science)

基　　金：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)。

摘　　要：研究电磁辐射下神经元的放电活动,对神经元相关的病变、控制和治疗具有极大的应用价值。基于理论分析与数值仿真方法,主要研究磁通HR神经元模型的分岔结构及其实现亚临界Hopf分岔稳定性控制。通过数值模拟发现该系统在双参数区域存在加周期1分岔、倍周期分岔与混沌交替现象。此外通过理论分析外界刺激电流的变化下系统平衡点的分布与稳定性,得出该系统存在超(亚)临界Hopf分岔点,并且在亚临界Hopf分岔点附近存在隐藏极限环吸引子。通过运用Washout控制器实现亚临界Hopf分岔稳定性控制,由此消除了隐藏放电现象,从而有助于揭示和理解神经元隐藏放电的产生和转变的内在机制。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.

关 键 词：双参数分岔分析 Hopf分岔分析 隐藏吸引子 Washout控制器 

分 类 号：O441[理学—电磁学] O193[理学—物理]