Center cyclicity of Lorenz, Chen and Lü systems

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2018-11-09Suggested citation
García, I. A. (Isaac A.);
Maza Sabido, Susanna;
Shafer, Douglas S.;
.
(2018)
.
Center cyclicity of Lorenz, Chen and Lü systems.
Nonlinear Analysis-Theory Methods & Applications, 2019, vol. 188, p. 362-376.
https://doi.org/10.1016/j.na.2019.06.012.
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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.
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Nonlinear Analysis-Theory Methods & Applications, 2019, vol. 188, p. 362-376European research projects
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