Bifurcation of Limit Cycles in Cubic Integrable Z2-Equivariant Planar Vector Fields

Abstract

In this paper, we study bifurcation of limit cycles in cubic planar integrable, non-Hamiltonian systems. The systems are assumed to be Z 2 -equivariant with two symmetric centers. Particular attention is given to bifurcation of limit cycles in the neighborhood of the two centers under cubic perturbations. Such integrable systems can be classified as 11 cases. It is shown that different cases have different number of limit cycles and the maximal number is 10. The method used in the paper relies on focus value computation.