Bifurcations Of Heterodimensional Cycle With Orbit Flip And Inclination Flip

In this paper we study the heterodimensional cycle with orbit flip and inclination flip in four dimension system. By setting up local moving frame systems in small tubular neigh-borhood of unperturbed heterodimensional cycle, we exhibit the relation formulas between the old coordinates and the new coordinates, construct a Poincare return map and further obtain the bifurcation equations. Based on the bifurcation analysis, we present the condi-tion for the existence and coexistence of the heterodimensional orbit, homoclinic orbit and periodic orbit, and then locate the bifurcation surfaces, existence regions and coexistence regions.