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Revista de Matemática Teoría y Aplicaciones
versão impressa ISSN 1409-2433
Rev. Mat vol.25 no.1 San José Jan./Jun. 2018
http://dx.doi.org/10.15517/rmta.v1i25.32230
Artículos
Tratamiento analítico de la bifurcación De hopf en una extensión del sistema de lü
Analytical treatment of the hopf Bifurcation in an extension of the lü system
1Facultad de Ciencias, Universidad del Tolima, Ibagué, Colombia. E-Mail: pecalderon@ut.edu.co
2Facultad de Matemáticas, Universidad Veracruzana, Xalapa, México. E-Mail: evmunoz@uv.mx
3Misma dirección que/Same address as: E. Muñoz-Aguirre. E-Mail: joalvarez@uv.mx
En este artículo se hace un análisis de la bifurcación de Hopf del sistema tridimensional tipo Lorenz introducido por Xianyi Li y Qianjun Ou (2011), este análisis consiste en identificar una región de parámetros del sistema donde la bifurcación de Hopf es no degenerada y supercrítica, aspecto que no es abordado en el artículo de Xianyi Li y Qianjun Ou. Para lograr este objetivo se utiliza el Teorema de la Variedad Central y el Teorema de Hopf. Además, para ilustrar los resultados, se muestran gráficas de algunas trayectorias del sistema, las cuales fueron obtenidas mediante simulación numérica.
Palabras clave: sistema tipo Lorenz; teorema de la variedad central; teorema de la bifurcación de Hopf
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
Referencias
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Recibido: 19 de Septiembre de 2016; Revisado: 27 de Junio de 2017; Aprobado: 16 de Diciembre de 2017