| Fitzhugh-Nagumo方程在非齐次边界条件下解的动力学分析 |
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| 引用本文： | 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]. 中北大学学报(自然科学版), 2012, 0(1): 43-46 |
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| 作者姓名： | 石丹青 柴玉珍 |
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| 作者单位： | 太原理工大学数学学院 |
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| 基金项目： | 太原理工大学校科技发展基金资助项目(博士启动费) |
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| 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.
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| 关 键 词： | Fitzhugh-Nagumo方程 稳定性 Lyapunov函数 Galerkin方法 |
Dynamics Analysis of Solutions for the Fitzhugh-Nagumo Equations with Inhomogeneous Boundary Conditions |
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| SHI Dan-qing,CHAI Yu-zhen. Dynamics Analysis of Solutions for the Fitzhugh-Nagumo Equations with Inhomogeneous Boundary Conditions[J]. Journal of North University of China, 2012, 0(1): 43-46 |
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| Authors: | SHI Dan-qing CHAI Yu-zhen |
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| Affiliation: | (College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China) |
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| 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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| Keywords: | Fitzhugh-Nagumo equations stability Lyapunov fuction Galerkin method |
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