Title :
The existence of closed trajectory in the van der Pol oscillator
Author :
Wang, Dongping ; Zhou, Shangbo ; Yu, Juebang
Author_Institution :
Coll. of Electr. & Inf. Eng., Sichuan Univ., Chengdu, China
fDate :
29 June-1 July 2002
Abstract :
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 (μ>0). By comparison, we find that, our method is natural and simple.
Keywords :
Poincare mapping; nonlinear network analysis; relaxation oscillators; Poincare-Bendixson theorem; VDP; audion circuit; closed trajectory; damping value; mathematical model; nonlinear differential equation; van der Pol oscillator; Circuits; Density estimation robust algorithm; Differential equations; Educational institutions; Integral equations; Limit-cycles; Mathematical model; Nonlinear equations; Oscillators; Trajectory;
Conference_Titel :
Communications, Circuits and Systems and West Sino Expositions, IEEE 2002 International Conference on
Print_ISBN :
0-7803-7547-5
DOI :
10.1109/ICCCAS.2002.1179089
