The existence of closed trajectory in the van der Pol oscillator

The van der Pol (VDP) equation is a nonlinear differential equation, and it is also the mathematical model for an audion circuit. It has given much attention by researchers and has been widely used in many fields. In this paper, using the noted Poincare-Bendixson theorem, we propose a new proof of the existence of closed trajectory in the van der Pol oscillator when damping value is positive (/spl mu/>0). By comparison, we find that, our method is natural and simple.