Limit Cycles Bifurcated from Some Z 4 -Equivariant Quintic Near-Hamiltonian Systems

Abstract

We study the number and distribution of limit cycles of some planar $Z_4$-equivariant quintic near-Hamiltonian systems. By the theories of Hopf and heteroclinic bifurcation, it is proved that the perturbed system can have 24 limit cycles with some new distributions. The configurations of limit cycles obtained in this paper are new.