Hindmarsh-Rose神经元模型的稳定性与Hopf分支  

Stability and Hopf bifurcation of Hindmarsh-Rose neuron model

作　　者：王晶囡[1] 李美华[1] 

机构地区：[1]哈尔滨理工大学应用数学系,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2016年第3期338-343,共6页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省青年科学基金资助项目(QC2014C003);黑龙江省教育厅科学技术研究项目(12541168)

摘　　要：研究外界刺激参数对Hindmarsh-Rose神经元模型的稳定性与产生Hopf分支的影响。通过导数法、特征值分析及Hurwitz判别准则,得到外界刺激与Hindmarsh-Rose模型平衡点个数变化、平衡点局部稳定性,及该模型在平衡点处经历Hopf分支之间的关系。运用Matlab进行数值仿真,验证了定理的结果,展示了当神经元受到较大外界刺激时出现的复杂现象。The effects of external stimuli parameters on the stability and Hopf bifurcation of the Hind- marsh-Rose neuron model are studied. Through the methods of derivative analysis, eigenvalue analysis and Hurwitz criterion, the relations between external stimuli parameters and the change of equilibrium number, the stability of equilibrium, as well as the occurrence conditions of Hopf bifurcation of Hind- marsh- Rose model are obtained. The Matlab numerical simulation is given to verify the theorem results, and show some complex phenomena about neurons stimulated by strong external stimuli.

关 键 词：Hindmarsh-Rose神经元模型 HOPF分支 稳定性 

分 类 号：O175.1[理学—数学] O193[理学—基础数学]