Work

Explicit formulas for two limit cycles of a family of planar differential systems

Year: 2025

Type: article

Abstract: In this work, we study a family of multi-parameter polynomial differential systems of degree eleven. We prove that the considered family has an invariant algebraic curve, which is given explicitly. Subsequently, we demonstrate the integrability of these systems and derive an explicit expression for a first integral. Moreover, we provide sufficient conditions for the systems to possess two explicitly given limit cycles. The applicability of our results is illustrated by a concrete example.

Source: Russian Mathematics

DOI: 10.26907/0021-3446-2025-4-71-79

Authors: S. E. Hamizi, R. Boukoucha

Institutions: Higher National School of Renewable Energies, Environment & Sustainable Development, University of Béjaïa

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4409844192

FWCI:

Cites: 12

Cited by:

Related to: 10