摘要
Hodgkin-Huxley(HH)神经模型是描述神经纤维中神经冲动传播的著名模型。FitzHugh-Nagumo(FHN)模型是对HH模型的一种简化。而Huxley方程是FHN方程的一种特殊情形。研究表明,Huxley方程也具有神经元模型的基本特征。以往对这些模型的研究常借助数值方法来实现,至今尚缺乏有效而简单的求解析解的方法。对Huxley方程的行波系统进行定性分析,该系统存在一端连接鞍点的有界异宿轨,进而选择奇点为鞍点的平面线性自治系统,利用该平面自治系统轨线向径的斜率,根据齐次平衡原则,构造出了Huxley方程行波系统的行波解。所用方法称为LS解法。
Hodgkin-Huxley（HH） nerve model is a famous model which is used to describe nerve impulse propagation in nerve fibre.FitzHugh-Nagumo（FHN） model is a simplification of HH model,and Huxley equation is a special case of FHN equation.It has been shown that Huxley equation possesses the basic characteristics of nerve model.Researching on these models was often carried out in virtue of numerical techniques in the past.And,in so for as is known,an efficient and simple method which can be used to obtain analytic solutions is lacking.Yet,a qualitative analysis on Huxley equation＇s traveling system has been carried through in this paper.There is a bounded heteroclinic orbit having its one end in connection with a saddle point for the traveling wave system.Then a linear plane autonomous system whose singular point is a saddle point is chosen.By means of the system orbit vector＇s slope,and according to homogeneous balance principle,the traveling wave solutions of Huxley equation＇s traveling system are constructed.The method used here is called LS method.
出处
《生物医学工程学杂志》
EI
CAS
CSCD
北大核心
2010年第5期1142-1145,共4页
Journal of Biomedical Engineering
基金
国家自然科学基金资助项目(10871129)
上海市重点学科建设项目资助(S30501)
上海市研究生创新基金项目资助(JWCXSL090114)
关键词
神经模型
Huxley方程
行波解
定性分析
LS解法
Nerve model； Huxley equation； Traveling wave solution； Qualitative analysis； LS method；
