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.

Keywords

• limit cycles
• polynomial differential systems
• averaging theory
• $(p
• q)$-trigonometric functions