title: [Research on a special model of nerve impulse propagation].
abstract: 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.
authors.affiliation: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China. lylxz@mail.haust.edu.cn
authors.forename: Xiangzheng
authors.initials: X
authors.lastname: Li
authors.forename: Weiguo
authors.initials: W
authors.lastname: Zhang
authors.forename: Sanling
authors.initials: S
authors.lastname: Yuan
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D001921:Brain / Q000502:physiology; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009431:Neural Conduction / Q000502:physiology*; D009474:Neurons / Q000502:physiology*