FitzHugh-Nagumo神经信息传导模型的数值模拟和分析

Numerical Simulation and Analysis of FitzHugh-Nagumo Nerve Information Conduction Model

神经系统是一个小型但复杂的综合系统,本文对FitzHugh-Nagumo神经信息传导模型,提出时间半隐欧拉格式的有限元算法.通过一维和二维的数值实验,验证了本文提出的时间空间离散格式数值求解FitzHugh-Nagumo神经元模型的有效性和可靠性,且与理论分析是一致的;同时,数值模拟可以在不知道神经元的空间结构和离子电流的情况下了解神经元是如何工作和处理信息的,有助于解释神经信息传导模型的一些生物学性质及复杂生物神经系统的信息传导等动力学行为.

The nervous system is a small but complex comprehensive system.In this paper,the finite element method of time semi-implicit Euler scheme is proposed for FitzHugh-Nagumo neuron model,and the convergence of the numerical method is analyzed.At last,one and two dimensional numerical experiments are given to verify the validity and reliability of the time-space discrete scheme proposed in this paper to numerically solve the FitzHugh-Nagumo neuron model,and it is consistent with the theoretical analysis.At the same time,numerical simulation can understand how neurons work and process information without knowing the spatial structure and ion current of neurons,which is helpful to explain some biological properties of neural information transmission models and dynamic behaviors such as information transmission in complex biological nervous systems.