IJPAM: Volume 6, No. 4 (2003)

THE UNIQUENESS OF LIMIT CYCLES FOR
A QUADRATIC SYSTEM WITH AN
INVARIANT STRAIGHT LINE

Yurong Zhou$^1$, Chengwen Wang$^2$Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Campus of Newark, Rutgers University - The State University of New Jersey, 312 Hill Hall, Newark, NJ 07102, USA
$^{1,2}$Department of Applied Mathematics
Shandong University of Science and Technology
Taian City, Shandong 271019, P.R. CHINA
$^2$Department of Mathematics and Computer Science
Faculty of Arts and Sciences
Campus of Newark
Rutgers University - The State University of New Jersey
312 Hill Hall, Newark, NJ 07102, USA


Abstract.In this paper, we first point out that the uniqueness of limit cycles for the quadratic system with an invariant straight line has not been completely proved. Then we introduce a new set of conditions that guarantee the uniqueness of limit cycles for Liénard systems and we use them to give a complete proof of the uniqueness theorem for quadratic invariant line equations.

Received: March 12, 2003

AMS Subject Classification: 34B15

Key Words and Phrases: quadratic differential system, limit cycle, orbit

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 6
Issue: 4