Heterodimensional Cycle Bifurcation With Two Negative Orbit Flip

In this paper,bifurcation of heterodimensional cycle with two negative orbit flip are investigated in the four-dimensional vector field.We get the bifurcation equations by set-ting up a local coordinate near the heterodimensional cycles and establishing the Poincare map.Then,by discussing the existence of sufficiently small nonnegative solutions,we provide the conditions for the existence,uniqueness and coexistence of the homoclinic loop,heteroclinic loop,periodic orbit and double periodic orbit under some generic hypotheses.The bifurcation surfaces and existence regions are also given.An example of application is also given to demonstrate our main result.