THE EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF PLANAR DIFFERENTIAL SYSTEMS

摘要

In this paper, we study a class of planar differential systems x = y(1 + ∑i=1∞bixi), y = -x + δy + a1x2 + a2xy + a3x2y + λx4exy. By using the Hopf bifurcation theory, some sufficient conditions for the existence and stability of limit cycles of such systems are obtained. Furthermore, by applying the L.A.Cherkas and L.I.Zheilevych's theorem about uniqueness, some sufficient conditions for the uniqueness of limit cycles of such systems are established.