Bifurcation Of Two Type Loops With Orbit And Inclination Flips

This thesis is devoted to investigate the bifurcations of homoclinic orbits and heteroclinic orbits.In chapter 1, the research background and development situation of bifurcation theory are given. We also introduce the main rusults achieved in this paper.In chapter 2, we are concerned with the heteroclinic loop bifurcations accompanied by one orbit flip and one inclination flip. And the heteroclinic loop have one nonhyperbolic equilibrium p1 and one hyperbolic saddle p2, where p1 is assumed to undergo transcritical bifurcation. we discuss bifurcations of heteroclinic loop when transcritical bifurcation hap-pens or does not happen, the persistence of heteroclinic loop, the existence of homoclinic loop and periodic orbit.In chapter 3, we investigate the homoclinic loop with orbit and inclination flips. we make a symmetrical transformation to it, then we can obtain a double homoclinic loops. The existense of periodic orbit and homoclinic orbit inside of two homoclinic loops and the coexistence of them are obtained. We also concern with the existence of periodic orbit and homoclinic orbit outside of double homoclinic loops and the coexistence of them.