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Bifurcations of Heteroclinic Loop with Twisted Conditions

The bifurcation problems of twisted heteroclinic loop with two hyperbolic critical points are studied for the case ρ11 > λ 11, ρ21 0 are the pair of principal eigenvalues of unperturbed system at the critical point pi, i = 1, 2. Under the transversal conditions, the authors obtained some results of the existence and the number of 1-homoclinic loop, 1-periodic orbit, double 1-periodic orbit, 2-homoclinic loop and 2-periodic orbit. Moreover, the relative bifurcation surfaces and the existence regions are given, and the corresponding bifurcation graphs are drawn.