Center Problems and Limit Cycle Bifurcations in a Class of Quasi-Homogeneous Systems

In this paper, we first classify all centers of a class of quasi-homogeneous polynomial differential systems of degree 5. Then we extend this kind of systems to a generalized polynomial differential system and provide the necessary and sufficient conditions to have a center at the origin. Furthermore, we study the Poincare bifurcation for its perturbed system as it has a center at the origin, find the Poincare cyclicity up to first order of e.

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