New criteria for the existence and non-existence of limit cycles in Liénard differential systems

Gasull Armengol , Giacomini Hector (1) , Llibre Jaume

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We provide several new criteria for the non-existence and the existence of limit cycles in Liénard differential systems. Some of these criteria generalize and improve previous ones. Their proofs are based on a general result for planar autonomous differential system that gives an upper bound for the number of limit cycles surrounding the same singular point.

Mots clés: limit cycles

Domaines: Systèmes dynamiques [math.DS]

Gasull Armengol, Giacomini Hector, Llibre Jaume. New criteria for the existence and non-existence of limit cycles in Liénard differential systems. Dynamical Systems, 2009, 24 (2), pp.171-185. ⟨10.1080/14689360802568086⟩. ⟨hal-01170579⟩