磁通e-HR神经元模型的Hopf分岔分析与控制  

Hopf bifurcation analysis and control of flux e-HR neuron model

作　　者：王红梅 安新磊[1] 乔帅 张薇 杨天宇 WANG Hongmei;AN Xinlei;QIAO Shuai;ZHANG Wei;YANG Tianyu(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China;School of Electronic Engineering,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070 [2]北京交通大学电子工程学院,北京100044

出　　处：《山东理工大学学报（自然科学版）》2020年第4期50-56,62,共8页Journal of Shandong University of Technology:Natural Science Edition

基　　金：中国博士后科学基金面上项目(2018M633649XB);甘肃省自然科学基金项目(17JR5RA096)。

摘　　要：神经元的放电模式与平衡点的分布及其它的分岔分析有关,本文通过引入磁通量来研究e-HR神经元模型的放电活动。在数值仿真与理论分析相结合的方法下,分析了在外界刺激电流的变化下神经元模型的平衡点分布与它的稳定性分析及其它的分岔分析。通过理论分析可知该系统存在亚临界Hopf分岔,并且在Hopf分岔点的附件发现了隐藏的极限环吸引子。运用Washout控制器使亚临界Hopf分岔转化为超临界Hopf分岔,从而使系统分岔点附近的拓扑结构发生转变,由此达到消除膜电压隐藏放电的目的。The discharge pattern of neurons is related to the distribution of equilibrium points and other bifurcation analysis. In this paper, the discharge activity of e-HR neuron model is studied by introducing magnetic flux. In this paper, the equilibrium point distribution, stability and other bifurcation analysis of the neuron model under the change of external stimulus current are analyzed by combining numerical simulation with theoretical analysis. The theoretical analysis shows that the system has subcritical Hopf bifurcation, and hidden limit cycle attractors are found in the attachment of the Hopf bifurcation point. Subcritical Hopf bifurcation is transformed into supercritical Hopf bifurcation by using Washout controller, so that the topological structure near the bifurcation point of the system is changed, thus eliminating the hidden discharge of membrane voltage.

关 键 词：电磁辐射 e-Hindmarsh-Rose神经元 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]