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

By Armengol Gasull and Hector Giacomini

Abstract

14 pages, O figuresInternational audienceWe 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

Topics: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
Publisher: 'American Institute of Mathematical Sciences (AIMS)'
Year: 2010
DOI identifier: 10.3934/dcds.2010.27.217
OAI identifier: oai:HAL:hal-00805731v1
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