Abstract

CALDERON-SAAVEDRA, Pablo Emilio; MUNOZ-AGUIRRE, Evodio  and  ALVAREZ-MENA, Jorge. Analytical treatment of the hopf Bifurcation in an extension of the lü system. Rev. Mat [online]. 2018, vol.25, n.1, pp.29-40. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v1i25.32230.

In this paper, we analyze Hopf Bifurcation of the three-dimensional Lorenz-like system introduced by Xianyi Li and Qianjun Ou (2011), this analysis consists of identifying a parameter region, in which the nondegenerate and supercritical Hopf bifurcation occurs, situation that is not discussed by Xianyi Li and Qianjun Ou. To achieve this purpose, we use the Center Manifold Theorem and the Hopf Theorem. In addition, to illustrate the results, the graphics of some trayectories of the system are shown, which were obtained via numerical simulations.

Keywords : Lorenz-type systems; center manifold theorem; Hopf bifurcation theorem.

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