A new class of planar differential systems with hyperbolic algebraic limit cycles

Abstract

This work investigates a family of planar polynomial differential systems of degree n or greater. For these systems, we introduce invariant algebraic curves of degree n that can exhibit closed connected components. We prove that each bounded component of such curves defines a hyperbolic limit cycle for the system. Furthermore, several explicit examples are provided to illustrate the validity and geometric applicability of our main theorem.