Upper bounds for the number of limit cycles of some planar polynomial differential systems

TL;DR

This paper introduces an effective method using Dulac functions and the Bendixson-Dulac Criterion to establish upper bounds on the number of limit cycles in certain planar polynomial differential systems, with applications to specific examples.

Contribution

It presents a novel approach to control the sign of functions in the Bendixson-Dulac Criterion, enabling better bounds on limit cycles in polynomial systems.

Findings

Successfully applied to multiple examples

Provided explicit upper bounds for limit cycles

Enhanced control over the sign of functions in the criterion

Abstract

We give an effective method for controlling the maximum number of limit cycles of some planar polynomial systems. It is based on a suitable choice of a Dulac function and the application of the well-known Bendixson-Dulac Criterion for multiple connected regions. The key point is a new approach to control the sign of the functions involved in the criterion. The method is applied to several examples.