Proving the existence of numerically detected planar limit cycles - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

Proving the existence of numerically detected planar limit cycles

Résumé

This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincar\'e--Bendixson regions by using transversal curves, that enables us to prove the existence of a limit cycle that has been numerically detected. We apply our results to several known systems, like the Brusselator one or some Li\énard systems, to prove the existence of the limit cycles and to locate them very precisely in the phase space. Our method, combined with some other classical tools can be applied to obtain sharp bounds for the bifurcation values of a saddle-node bifurcation of limit cycles, as we do for the Rychkov system.

Dates et versions

hal-01292647 , version 1 (23-03-2016)

Identifiants

Citer

Gasull Armengol, Hector Giacomini, Grau Maite. Proving the existence of numerically detected planar limit cycles. 2016. ⟨hal-01292647⟩
134 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More