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.