Center cyclicity of Lorenz, Chen and Lü systems. (November 2019)

• Record Type: Journal Article
• Authors: García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 362
• Page End: 376
• Publication Date: 2019-11
• Subjects: 37G15 -- 37G10 -- 34C07 -- 34C23; Cyclicity -- Limit cycle -- Center -- Center manifold; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.06.012
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This work provides upper bounds on the cyclicity of the centers on center manifolds in the well-known Lorenz family, and also in the Chen and Lü families. We prove that at most one limit cycle can be made to bifurcate from any center of any element of these families, perturbing within the respective family, with the exception of one specific Lorenz system where the cyclicity increases. We also show that this bound is sharp.