| 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. |
