Two Types Of Higher Polynomial System With Multiple Limit Cycle

In this paper, by using the qualitative theories and bifurcation method of ordinary differential equations, two planar polynomial systems are studied, qualitative behaviors of trajectories are obtained. The whole paper consists of three chapters.The first chapter is the introduction, in which we mainly introduce the developing history and the present progress of center and bifurcation theories, some fundamental definitions and lemmas of dynamics systems such as bifurcation and stability theory that can be used in this paper, and briefly represent the main works of the thesis.In the second chapter, a class of seven orders polynomial system has been studied. We research its singularity value and center conditions of the infinite singular points of the system. So we obtain its seven singularity value and give the sufficient condition when the infinite singular point is a center. Then we prove that the system bifurcate foue limit cycles around infinity.In the third chapter, we studied the condition when O(0,0) is a center and the limit cycles bifurcated from O(0,0) of a class of ive orders polynomial system. By using the method of bifurcation theory, we give the conditions that three limit cycles bifurcated from 0(0,0).