Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 15, pp. 1-12.

Title: Cubic and quartic planar differential systems with exact
       algebraic limit cycles

Authors: Ahmed Bendjeddou (Univ. de Setif, Algerie)
         Rachid Cheurfa   (Univ. de Setif, Algerie)

Abstract: 
 We construct  cubic and quartic polynomial planar differential
 systems with exact limit cycles that are ovals of algebraic real
 curves of degree four. The result obtained for the cubic case
 generalizes a proposition of [9]. For the quartic case, we deduce
 for the first time a class of systems with four algebraic limit
 cycles and another for which nested configurations of limit
 cycles occur.
 	 
Submitted April 28, 2010. Published January 26, 2011.
Math Subject Classifications: 34C05, 34A34, 34C25.
Key Words: Polynomial system; invariant curve; algebraic curve;
           limit cycle; Hilbert 16th problem.