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

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

2008-03-14

arxiv.org/abs/0803.2209v1

Mathematics

Dynamical Systems

14 pages, O figures

Scientific paper

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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