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

2008/03/14 by Armengol Gasull, Gasull, Armengol, Hector Giacomini +1
Mathematics · #34C05 #34C07 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS #msc:34C05 #msc:34C07

paper · pdf · doi:10.48550/arxiv.0803.2209

14 pages, O figures

arxiv created 2008/03/14 · arxiv updated 2009/12/01

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.

Related

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• Proving the existence of numerically detected planar limit cycles
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