Tratamiento analítico de la bifurcación de hopf en una extensión del sistema de lü

• Autores: Pablo Emilio Calderón Saavedra, Evodio Muñoz Aguirre, Jorge Álvarez Mena
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 25, Nº. 1, 2018, págs. 29-40
• Idioma: español
• DOI: 10.15517/rmta.v1i25.32230
• Títulos paralelos:
  • Analytical treatment of the hopf bifurcation in an extension of the lü system
• Enlaces
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• Resumen
  • español

    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 mediantesimulación numérica.

  • English

    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.

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