Bifurcations Of Double Homoclinic Loops With Nonresonant Eigenvalues And Inclination Flip

In this work, codimension 3 bifurcations of double homoclinic loops with nonresonant eigenvalues and inclination flip in four dimensional systems are studied. The Poincar′e map is established to solve various problems in double-homoclinic-loop bifurcations with codimension 3. The existence, nonexistence, coexistence, incoexistence and uniqueness of large 1-hom orbit and large1-per orbit near Γ = Γ1 ∪Γ2 is given. At last, an analytical example is given to illustrate our main results.