Hopf Bifurcations Of Two Polynomial Differential Systems

This paper contains four parts:In the first part,we will give some basic knowledge on Hopf bifurcation. At the same time we will give a brief description of the known results and the results that I have got on the systems that we will discuss. The third part mainly studies the Hopf bifurcation and limit cycle of a three-dimensional polynomial differential system. We will give the conditions for existence and the stability of the periodic orbits bifurcated from Hopf bifur-cation. The fourth part mainly deals with the Hopf bifurcation of the system coupled by Brusselator Oscillators.