Fitzhugh-Nagumo方程在非齐次边界条件下解的动力学分析

石丹青; 柴玉珍

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Fitzhugh-Nagumo方程在非齐次边界条件下解的动力学分析

更新时间：2026-09-14

- Fitzhugh-Nagumo方程在非齐次边界条件下解的动力学分析
- Fitzhugh-Nagumo方程在非齐次边界条件下解的动力学分析
- Issue 1, (2012)
- 作者机构：
  
  太原理工大学数学学院
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- Published：2012
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石丹青, 柴玉珍. Fitzhugh-Nagumo方程在非齐次边界条件下解的动力学分析[J]. 2012, (1).
DOI：

石丹青, 柴玉珍. Fitzhugh-Nagumo方程在非齐次边界条件下解的动力学分析[J]. 2012, (1). DOI：

摘要

Hodgkin-Huxley方程描述了生物神经的放电活动

Fitzhugh-Nagumo方程是Hodgkin-Huxley方程的简化模型.讨论了Fitzhugh-Nagumo神经传导方程在非齐次边界条件下的初边值问题

利用Galerkin方法证明了Fitzhugh-Nagumo方程在非齐次边界条件下整体解的存在性和唯一性;运用Lyapunov稳定性理论对Fitzhugh-Nagumo方程进行了稳定性分析.

Abstract

Hodgkin-Huxley equation describes the discharge activity of biological neural.Fitzhugh-Nagumo equation is a simplified model of Hodgkin-Huxley equation.The initial-boundary value problems of the Fitzhugh-Nagumo nerve conduction equation with inhomogeneous boundary conditions were discussed.The existence and uniqueness of the global solutions for the Fitzhugh-Nagumo equation with inhomogeneous boundary conditions was proved by means of the Galerkin method.The stability of Fitzhugh-Nagumo equation was analyzed by means of the Lyapunov stability theory.

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