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Bifurcation of limit cycles near heteroclinic loops in near-Hamiltonian systems. (English) Zbl 1461.34062

In this paper, a method for calculating the expansion coefficients of the first order Melnikov function is proposed, which is suitable for the near-Hamiltonian system near the polycycle with hyperbolic saddles. With more those coefficients, more limit cycles could be determined around the polycycle. The limit cycles generated from a heteroclinic cycle with two saddles is taken as an example to illustrate the method. The result is new and interesting.

MSC:

34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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