Bifurcation Of Rough Heteroclinic Loop With Two Orbit Flips

In this paper, heteroclinic loop bifurcations with two orbit flips are in-vestigated in a four dimensional vector fields. We get the bifurcation equations by setting up a local coordinate near the rough heteroclinic orbit and estab-lishing the Poincare map. The persistence of heteroclinic orbit, the existence of homoclinic orbits, the noncoexistence of heteroclinic loop and periodic orbit or homoclinic orbit, the noncoexistence and coexistence of heteroclinic and periodic orbit,homoclinic orbits and periodic orbit are obtained by study-ing the corresponding bifurcation equations. The approximate expressions of correspomding bifurcation curves (or surfaces) are also given. An example of application is also given to domonstrate our main results.