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Codimension 3 nontwisted double homoclinic loops bifurcations with resonant eigenvalues. (English) Zbl 1195.34058
Summary: This paper presents nontwisted double-homoclinic-loop bifurcations with resonant eigenvalues in four dimensional vector fields. The Poincaré map is established to solve various problems in double-homoclinic-loop bifurcations with codimension 3. Bifurcation diagrams and bifurcation curves are given.
MSC:
34C23Bifurcation (ODE)
34C37Homoclinic and heteroclinic solutions of ODE
37G20Hyperbolic singular points with homoclinic trajectories
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