Bifurcations Of Rough Heteroclinic Loops With Two Saddle Points With Higher Dimensions

In the dissertation,we consider the unperturbed system of two singular pointswith two connecting heteroclinic trajectories. If we give it a small disturbance, wewill derive the bifurcation problems. We obtain P oincar′emap and bifurcation equa-tions by establishing the local coordinate and using the transformation of Silnikovcoordinate. According to discussing the existence of positive solutions or zero solu-tions of the bifurcation equations, we will obtain l homoclinic orbit,1heteroclinicloop and1-periodic orbit of the existence, nonexistence, coexistence and uniqueness.Moreover, we gain the existence conditions of2-periodic orbit and2homoclinic,and the bifurcation surface and the bifurcation problems.In the first chapter, research background and definitions and some notationsand which are mentioned in the Paper, at the same time, the main results andinnovation of the paper are introduced.The second chapter will spread out in the round of specific practice as follows:The first section, we consider system as follows:and unperturbed system as follows:We putthe system into a standard type with the assumptions.We obtain P oincar′e map and bifurcation equations by establishing the localcoordinate and using the transformation of Silnikov coordinate.The third section and the fourth section accordingly discusses the bifurcationequation with nontwisted and twisted cases. Then we will obtain l homoclinic orbit,1heteroclinic loop and1periodic orbit of the existence, nonexistence, coexistenceand uniqueness. Moreover, we gain the existence conditions of2periodic orbit and2homoclinic, and the bifurcation surface and the bifurcation problems.