中文摘要：

研究了神经元Chay模型的动力学.首先在Mathematica软件的辅助下找出系统在给定参数下的平衡点,并根据其Jacobian矩阵得到平衡点的稳定性.然后利用Hopf分岔理论得出Hopf分岔的存在性,并且利用Hopf分岔分析得出分岔方向和分岔周期解的稳定性.最后使用WinPP软件给出了支持理论分析的数值模拟.结果表明:Chay模型存在唯一平衡点,在系统控制参数的变化下,产生超临界Hopf分岔,系统由存在稳定的周期解和不稳定的平衡点过渡为周期解消失,平衡点渐近稳定.因此,Ca2+对神经元细胞的影响是巨大的.

英文摘要：

The dynamics of the neuronal Chay model is analyzed.With the help of software Mathematica,the unique equilibrium point of the Chay model under the considered parameters is found,and the stability of equilibrium point is established according to its Jacobian matrix and eigenvalues.Then,the Hopf bifurcation theory is used to verify the existence of Hopf bifurcation and explore the bifurcation direction and the stability of the bifurcating periodic solutions.Finally,the software WinPP is employed to support th...