Bifurcations of limit circles and center conditions for a class of non-analytic cubic Z 2 polynomial differential systems

In this paper, bifurcations of limit cycles at three fine focuses for a class of Z 2-equivariant non-analytic cubic planar differential systems are studied. By a transformation, we first transform nonanalytic systems into analytic systems. Then sufficient and necessary conditions for critical points of the systems being centers are obtained. The fact that there exist 12 small amplitude limit cycles created from the critical points is also proved. Henceforth we give a lower bound of cyclicity of Z 2-equivariant non-analytic cubic differential systems.