Upper bounds for the number of limit cycles of someplanar polynomial differential systems

Armengol Gasull; Hector Giacomini

doi:10.3934/dcds.2010.27.217

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2010, Volume 27, Issue 1: 217-229. Doi: 10.3934/dcds.2010.27.217

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

Armengol Gasull^1, and
Hector Giacomini^2,

1.
Dept. de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona
2.
Laboratoire de Mathématique et Physique Théorique, C.N.R.S. UMR 7350, Faculté des Sciences et Techniques, Université de Tours, Parc de Grandmont,37200 Tours

Received: July 2009

Revised: November 2009

Published: March 2010

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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.

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Mathematics Subject Classification: Primary: 34C05, 34C07; Secondary: 37C27.

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