Universitat de Lleida
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.
The first and second authors are partially supported by a MINECO grant number MTM2017-84383-P and an AGAUR grantnumber 2017SGR-1276.
Anglès
Cyclicity; Limit cycle; Center
Elsevier
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-84383-P/ES/ORBITAS PERIODICAS E INTEGRABILIDAD EN SISTEMAS DIFERENCIALES CONTINUOS/
Versió postprint del document publicat a https://doi.org/10.1016/j.na.2019.06.012
Nonlinear Analysis-Theory Methods & Applications, 2019, vol. 188, p. 362-376
cc-by-nc-nd (c) Elsevier, 2019
http://creativecommons.org/licenses/by-nc-nd/3.0/es
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