Center cyclicity of Lorenz, Chen and Lü systems

García, I. A. (Isaac A.); Maza Sabido, Susanna; Shafer, Douglas S.

doi:https://doi.org/10.1016/j.na.2019.06.012

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Issue date

2018-11-09

Author

García, I. A. (Isaac A.)

Maza Sabido, Susanna

Shafer, Douglas S.

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.