电场作用下HR神经元的分岔分析及参数辨识  

Bifurcation analysis and parameter identification of HR neurons under electric field

作　　者：肖冉 安新磊[1] 祁慧敏 乔帅 XIAO Ran;AN Xinlei;QI Huimin;QIAO Shuai(School 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,甘肃兰州730070

出　　处：《浙江大学学报（理学版）》2022年第6期691-697,705,共8页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11962012)。

摘　　要：详细分析了电场作用下四维Hindmarsh-Rose (HR)神经元模型的分岔模式及放电行为。通过数值仿真得到该神经元模型的多组双参数分岔图、最大Lyapunov指数图、峰峰间期分岔图等,发现该模型在双参数平面上存在倍周期分岔、加周期分岔等模式及“锯齿状”混沌结构。通过构建合适的目标函数,提出了自适应混合粒子群遗传算法,将神经元模型的参数辨识转化为最优化问题。数值仿真结果表明,算法对神经元模型的参数辨识效果较好,能更准确地辨识未知参数,具有一定优越性。The bifurcation mode and firing behavior of the four-dimensional Hindmarsh-Rose(HR) neuron model under electric field are analyzed in detail. Several groups of bifurcation diagrams of the neural system with two parameters are derived by numerical simulation, which correspond to the maximum Lyapunov exponent diagram and the ISI bifurcation diagram. It is found that the system has period-doubling bifurcation, period-adding bifurcation and chaotic structure with "jaggedness" on the biparametric plane. Since parameter identification of neuron model is an important part of neuron dynamics analysis, by constructing a suitable objective function, we propose an adaptive hybrid particle swarm genetic algorithm to convert the parameter identification problem of neuron model into an optimization problem. Numerical simulation results show that the proposed algorithm is effective and feasible in the parameter identification of neuron model.

关 键 词：HR神经元 双参数分岔 混合粒子群遗传算法 参数辨识 

分 类 号：O441[理学—电磁学]