适应性神经元模型的Hopf分岔迁移控制  

Migration Control of Hopf Bifurcation Based on Adaptive Neuron Model

作　　者：袁春华 冯博文 李翔宇 YUAN Chunhua;FENG Bowen;LI Xiangyu(Shenyang Ligong University,Shenyang 110159,China)

机构地区：[1]沈阳理工大学自动化与电气工程学院,沈阳110159

出　　处：《沈阳理工大学学报》2022年第2期1-6,共6页Journal of Shenyang Ligong University

基　　金：国家自然科学基金项目(62173073);辽宁省教育厅科学研究项目计划(LG202028);沈阳理工大学高水平成果建设计划资助项目(SYLUXM202109)。

摘　　要：神经元模型相轨迹的质变是由于神经元动力学经历了分岔过程,分岔类型决定了神经元的兴奋性质。适应性是神经元的普遍特性,本文在二维Prescott神经元模型的基础上引入适应性电流,将三维Prescott模型作为研究对象,采用解析与数值模拟相结合的方法,研究了适应性神经元模型的Hopf分岔特性,并对模型施加了线性状态反馈进行迁移控制,改变了模型发生Hopf分岔的位置;对模型同时施加线性反馈控制和非线性反馈控制,不仅改变了模型Hopf分岔的发生位置,同时改变了Hopf分岔的类型,使亚临界Hopf分岔变为超临界Hopf分岔。The qualitative change of the phase trajectory of the neuron model is due to the bifurcation process of neuron dynamics,and the type of bifurcation determines the excitability of the neuron.Adaptability is a universal characteristic of neurons.In this paper,adaptive current is introduced on the basis of the two-dimensional Prescott neuron model,and the three-dimensional Prescott model is used as the research object.The method of combining analysis and numerical simulation is used to study the Hopf bifurcation characteristics of adaptive neuron model.The linear state feedback is applied to the model for migration control,which changes the position of the Hopf bifurcation of the model.Finally,linear feedback control and nonlinear feedback control are applied to the model at the same time,which not only changes the location of the Hopf bifurcation of the model,but also changes the type of Hopf bifurcation,turning the subcritical Hopf bifurcation into a supercritical Hopf bifurcation.

关 键 词：HOPF分岔 Prescott神经元模型 适应性 迁移控制 

分 类 号：Q424[生物学—神经生物学]