IJPAM: Volume 29, No. 4 (2006)

RIVER AND THE CRITICAL POINT AT INFINITY IN
THE PLANAR QUADRATIC DIFFERENTIAL SYSTEMS

Abdelkader Bouhassoun
Department of Mathematics
University of Oran Senia
P.O. Box 1524, Oran, 31000, ALGERIA
e-mail: bhsn58@yahoo.fr


Abstract.In this paper, quadratic polynomial differential systems of the form: $X'=P(X,Y)$, $Y'=Q(X,Y)$ defined in $R^{2}$ are discussed. We will see that, for some quasi homogeneous vector fields, the river phenomenon can exist. We will give thus a sufficient conditions for their existence by studying the critical points at infinity.

Received: April 26, 2006

AMS Subject Classification: 34C05, 34C025, 34D05, 34D15

Key Words and Phrases: singular perturbation, slow curve, fast-slow system, asymptotic properties

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 29
Issue: 4