Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems

Abstract

In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented. As an improvement, we obtain by a new method a similar result for a family of quintic polynomial differential systems.

Keywords

• Non-algebraic limit cycle
• invariant curve
• Poincare return-map
• first integral
• Riccati equation