The uniqueness of limit cycles for a generalized Rayleigh–Liénard oscillator

The aim of this paper is to investigate limit cycles of the generalized Rayleigh–Liénard oscillator \(\dot{x}=\varphi (y)\) $\dot{x}=\phi (y)$ , \(\dot{y}=-g(x)-f(x,y)y\) $\dot{y}=-g(x)-f(x,y)y$ . A criterion on the uniqueness and stability of limit cycles is given. We apply the criterion to two generalized Rayleigh–Liénard systems and get the uniqueness of limit cycles. Moreover, the stability and locations of limit cycles are obtained if they exist.