Center cyclicity of Lorenz, Chen and Lü systems

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.

The first and second authors are partially supported by a MINECO grant number MTM2017-84383-P and an AGAUR grantnumber 2017SGR-1276.