IJPAM: Volume 59, No. 4 (2010)

ON THE EXISTENCE OF EXACTLY $N$ LIMIT CYCLES
IN LIENARD SYSTEMS

Aniruddha Palit$^1$, Dhurjati Prasad Datta$^2$
$^1$Department of Mathematics
Surya Sen Mahavidyalaya
Siliguri, West Bengal, PIN-734004, INDIA
e-mail: mail2apalit@gmail.com
$^2$Department of Mathematics
University of North Bengal
P.O. North Bengal University, Raja Rammohunpur
Dist. Darjeeling, West Bengal, PIN-734013, INDIA
e-mail: dp_datta@yahoo.com


Abstract.A theorem on the existence of exactly $N$ limit cycles around a critical point for the Lienard system $\ddot{x}+f\left( x\right) \dot{x}+g\left( x\right) =0$ is proved. An alogrithm on the determination of a desired number of limit cycles for this system has been considered which might become relevant for a Lienard system with incomplete data.

Received: February 6, 2010

AMS Subject Classification: 34A34, 70K05

Key Words and Phrases: autonomous system, Lienard equation, limit cycle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 4