Cubic and quartic planar differential systems with exact algebraic limit cycles

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.

Keywords

• Polynomial system
• invariant curve
• algebraic curve
• limit cycle
• Hilbert 16th problem