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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 ${\rho }_{1}^{1}>{\lambda }_{1}^{1},{\rho }_{2}^{1}<{\lambda }_{2}^{1},{\rho }_{1}^{1}{\rho }_{2}^{1}<{\lambda }_{1}^{1}{\lambda }_{2}^{1}$, where - ${\rho }_{i}^{1}$ <0 and ${\lambda }_{i}^{1}$ >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:
 37G20 Hyperbolic singular points with homoclinic trajectories 34C37 Homoclinic and heteroclinic solutions of ODE 34C23 Bifurcation (ODE)
##### References:
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