Homoclinic Bifurcation of Orbit Flip with Resonant Principal Eigenvalues

Codimension–3 bifurcations of an orbit–flip homoclinic orbit with resonant principal eigenvalues are studied for a four–dimensional system. The existence, number, co–existence and non–coexistence of 1–homoclinic orbit, 1–periodic orbit, 2n–homoclinic orbit and 2n–periodic orbit are obtained. The bifurcation surfaces and existence regions are also given.