神经脉冲波传播形态的研究

Study on Propagation Form of Nerve Impulse Waves

Hodgkin-Huxley模型(H-H模型)是研究神经电生理不可或缺的数学依据。但是,到目前为止,对H-H神经元模型的分析缺少解析研究。本文对经典的H-H模型进行具体分析,得到简化H-H模型以及Nagumo方程,利用齐次平衡方法首次求出简化H-H方程和Nagumo方程的孤波解。研究表明:神经冲动可以孤波的模式传播。

Hodgkin-Huxley model is the indispensable mathematics basis for the study of neuro-electro-physiology. But so far, there is few analytic study about H-H neuron model. In this paper, the features of the classical H-H model are analyzed, and then a simplified H-H model and Nagurno equation are proposed, and their solitary wave solutions are first obtained with the homogeneous balance method. The study shows that nerve impulse may propagate with the mode of solitary wave.