一类三维神经元模型的分支研究

Bifurcation Analysis of a Three-Dimensional Neuron Model

考虑一类三维神经元模型的分支问题.利用常微分方程的定性与分支理论的知识,讨论了模型的平衡点个数及其稳定性,主要分析了平衡点的Hopf分支和Bogdanov-Takens分支,并得到了相应的鞍结点分支曲线,Hopf分支曲线与同宿分支曲线.

This paper consider a three-dimensional neuron model.By using the bifurcation theory of differential equations,we discuss the stability,the Hopf bifurcation and the BogdanovTakens bifurcation of equilibria.We obtain the saddle-node bifurcation curve,the Hopf bifurcation curve and the Homoclinic bifurcation curve near the Bogdanov-Takens point.