Some Applications of the Extended Bendixson-Dulac Theorem

TL;DR

This paper presents a unified approach using an extended Bendixson-Dulac Theorem to analyze the number of limit cycles in planar vector fields, including proofs and applications.

Contribution

It introduces a unified framework for applying the extended Bendixson-Dulac Theorem to various families of planar vector fields, with new proofs and applications.

Findings

Unified approach to limit cycle analysis

New proofs of existing results

Multiple applications demonstrated

Abstract

During the last years the authors have studied the number of limit cycles of several families of planar vector fields. The common tool has been the use of an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this work is to present an unified approach of some of these results, together with their corresponding proofs. We also provide several applications.