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Codimension 2 bifurcations of double homoclinic loops. (English) Zbl 1197.37065

Summary: The double-homoclinic-loop bifurcations in four dimensional vector fields are investigated by setting up local coordinates near the double homoclinic loops. We get the existence, uniqueness and incoexistence of the large 1-hom and large 1-per orbit, and their corresponding existence regions are located. Furthermore, the inexistence of the large 2-hom and large 2-per orbit are also demonstrated.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
37G15Bifurcations of limit cycles and periodic orbits
34C23Bifurcation (ODE)
34C37Homoclinic and heteroclinic solutions of ODE
37C29Homoclinic and heteroclinic orbits