Heteroclinic loop bifurcations by perturbing a class of Z2-equivariant quadratic switching Hamiltonian systems with nilpotent singular points

Abstract

This paper investigates the problem of heteroclinic loop bifurcation by perturbing a class of Z2-equivariant quadratic switching systems with nilpotent singular points. Firstly, it provides sufficient and necessary conditions for the occurrence of a heteroclinic loop. Next, the system is perturbed by piecewise polynomial systems of degree n≥1. The paper then considers the lower bound for the maximum number of limit cycles that bifurcate from the generalized heteroclinic loop, finding at least n+[n2] limit cycles.