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Bifurcations of rough heteroclinic loop with two saddle points. (English) Zbl 1215.37039
Summary: The bifurcation problems of rough 2-point-loop are studied for the case ρ 1 1 >λ 1 1 ,ρ 2 1 <λ 2 1 ,ρ 1 1 ρ 2 1 <λ 1 1 λ 2 1 , where - ρ i 1 <0 and λ i 1 >0 are the pair of principal eigenvalues of unperturbed system at saddle point p i , i=1,2. Under the transversal and nontwisted conditions, the authors obtain some results of the existence of one 1-periodic orbit, one 1-periodic and one 1-homoclinic loop, two 1-periodic orbits and one 2-fold 1-periodic orbit. Moreover, the bifurcation surfaces and the existence regions are given, and the corresponding bifurcation graph is drawn.
MSC:
37G20Hyperbolic singular points with homoclinic trajectories
34C37Homoclinic and heteroclinic solutions of ODE
34C23Bifurcation (ODE)
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