Bifurcations Of Heterodimensional Cycles With One Orbit Flip

In this paper, bifurcations of heterodimensional cycles with one orbit flip are investigated in a three dimensional vector fields. We get the bifur-cation equations by setting up a lacal coordinate near the rough heteroclinic orbit and establishing the Poincare map. Then, by discussing the existense of sufficiently small nonnegative solutions, the persistence of heteroclinic loop, the existence of homoclinic loop and periodic orbit, and the coexistence of het-eroclinic loop and periodic orbit are established. The approximate expressions of corresponding bifurcation curves or surfaces are also given. An example of application is also given to demonstrate our main results...