Isolated periodic wave trains in a generalized Burgers–Huxley equation

We study the isolated periodic wave trains in a class of modified generalized Burgers–Huxley equation. The planar systems with degenerate equilibrium arising after traveling transformation are investigated. By finding certain positive definite Lyapunov functions neighborhood singular points and Hopf bifurcation points, number possible limit cycles corresponding is determined. existence equation established, which universal for any integer n this model. Within process, one interesting example obtained, namely series bifurcating from semi-hyperbolic point zero eigenvalue non-zero its Jacobi matrix.