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

Armengol Gasull , Hector Giacomini (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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.

Domaines: Systèmes dynamiques [math.DS]; Analyse classique [math.CA]

Armengol Gasull, Hector Giacomini. Upper bounds for the number of limit cycles of some planar polynomial differential systems. Discrete and Continuous Dynamical Systems - Series A, 2010, 27 (1), pp.217-229. ⟨10.3934/dcds.2010.27.217⟩. ⟨hal-00805731⟩