Hopf Bifurcation Of Traveling Wave Solution Of Fitzhugh-nagumo System

In this thesis, we mainly study Hopf bifurcation of traveling wave solution of FitzHugh-Nagumo system. When we consider traveling wave, FitzHugh-Nagumo system can be changed into three-dimensional nonlinear ordinary differential equa-tions, which is analyzed by higher-dimension Hopf bifurcation. With Center mani-fold theorem and Lyapunov coefficient method, the first three facal values is given, which means that there exist three small amplitude periodic solutions around a singular point of the system with some parameters in00,d>0. on the other hand, the system possesses two limit cycles around two singular points simultaneously with a=-1. Therefore, it is proved FitzHugh-Nagumo system has the periodic wave with frequencies.