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

This paper investigates the problem of heteroclinic loop bifurcation by perturbing a class of Z(2)-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 + [ n/2 ] limit cycles.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the problem of heteroclinic loop bifurcation by perturbing a class of Z(2)-equivariant quadratic switching systems with nilpotent singular points. It provides sufficient and necessary conditions for the occurrence of a heteroclinic loop, and finds the lower bound for the maximum number of limit cycles that bifurcate from the generalized heteroclinic loop.