Electronic Journal of Qualitative Theory of Differential Equations (Feb 2016)
Limit cycles for a class of polynomial differential systems
Abstract
In this paper, we consider the limit cycles of a class of polynomial differential systems of the form $\dot{x}=-y^{2p-1},\ \dot{y}=x^{2mp-1}+\varepsilon(px^{2mp}+qy^{2p})(g(x,y)-A)$, where $g(x,y)$ is a polynomial. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of a center using the averaging theory of first order.
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