AI Article Synopsis
- The Hodgkin-Huxley (HH) model describes nerve impulse propagation, while the FitzHugh-Nagumo (FHN) model simplifies it, with the Huxley equation being a special case of FHN.
- Research on these models was primarily done using numerical methods, and there has been a lack of efficient analytic solutions.
- This paper presents a qualitative analysis of the Huxley equation, identifying a bounded heteroclinic orbit and constructing traveling wave solutions using the LS method.
Article 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.
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