电磁场效应下HR神经元的全局分岔与参数辨识  

GLOBAL BIFURCATION AND PARAMETER IDENTIFICATION OF HR NEURONS UNDER ELECTROMAGNETIC FIELD EFFECTS

作　　者：肖冉 安新磊[1] 祁慧敏 Xiao Ran;An Xinlei;Qi Huimin(College of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《动力学与控制学报》2021年第5期81-88,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11962012);中国博士后科学基金资助项目(2018M633649XB)。

摘　　要：详细分析了在磁通变量和电场变量共同作用下五维Hindmarsh-Rose(HR)神经元模型的全局分岔行为.通过数值仿真的方法,做出该神经元系统的双参数分岔图、峰峰间期(ISI)分岔图和最大Lyapunov指数图,发现该系统在双参数平面上具有倍周期分岔、逆倍周期分岔、加周期分岔等分岔模式以及呈“锯齿状”的混沌结构.此外,基于Lyapunov稳定性理论以及自适应同步的方法,以混沌态时的系统为驱动系统,构建对应的响应系统,选择合适的控制器,实现了驱动系统与响应系统的同步,并辨识出未知参数.数值模拟证明了此方法的有效性和可行性.In this paper,global bifurcation behavior of five-dimensional Hindmarsh-Rose(HR)neuron model is analyzed in detail under the interaction of magnetic flux and electric field variables.By means of numerical simulation,biparametric bifurcation diagram,ISI bifurcation diagram and maximum Lyapunov exponent diagram of the neuron system are constructed,and it is found that the system has period-doubling bifurcation,inverse period-doubling bifurcation,period-adding bifurcation and chaotic structure with"jaggedness"on the biparametric plane.In addition,based on the stability theory of Lyapunov and the idea of adaptive synchronization,the corresponding response system is constructed by taking the chaotic system as a driving system,and an appropriate controller is selected to realize synchronization between the driving system and the response system,with unknown parameters were identified.Numerical simulation shows effectiveness and feasibility of this method.

关 键 词：双参数分岔分析 倍周期分岔 自适应同步 参数辨识 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]