神经元模型的稳定性分析与Hopf分岔控制  

The stability analysis and control of Hopf bifurcation of a neuron model

作　　者：袁春华[1] 王江[1] 

机构地区：[1]天津大学电气与自动化工程学院,天津300072

出　　处：《振动工程学报》2015年第1期52-58,共7页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(61072012)

摘　　要：根据Poincare Birkhoff(PB)规范形理论,研究了神经元模型的Hopf分岔类型的判定与分岔控制问题。分析了离子电流与电导对神经元平衡点变化与分岔点分布的影响,计算了神经元最小模型亚临界Hopf分岔的稳定性指标,并在此基础上建立了神经元最小模型的分岔控制方程,利用Washout控制器实现了对该神经元模型亚临界Hopf分岔的控制。研究表明:在给定的参数范围内,该神经元模型发生了2次亚临界Hopf分岔。提出的解析与数值相结合的Hopf分岔稳定性判定方法可以确定最小神经元模型的Hopf分岔的稳定性,基于稳定性判定指标和Washout控制器的分岔控制方法可以实现对神经元增幅放电的有效控制。According to Poincare Birkhoff（PB）normal form theory,the type identification and the control of Hopf bifurcation of a neuron model were studied.The effects of ion currents and conductance on equilibrium points and bifurcation points were analyzed.The subcritical Hopf bifurcation stability index of the neuron model was calculated.A Hopf bifurcation control of equation of the minimal neuron model was established accordingly,using Washout controller to implement the subcritical Hopf bifurcation control of the neuron model.It is shown that the subcritical Hopf bifurcation of the neuron model occurs two times in a given range of parameters.The method that combines the analytical and numerical indicators to determine the stability of the Hopf bifurcation presented here can determine the Hopf bifurcation stability of the minimal neuron models.The increasing firing type of the neuron can be effectively controlled based on the stability determination index and the Washout ontroller.

关 键 词：非线性系统 神经元模型 HOPF分岔 稳定性判定指标 Washout分岔控制 

分 类 号：O231.2[理学—运筹学与控制论] TP13[理学—数学]