<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332018000100029</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v1i25.32230</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Tratamiento analítico de la bifurcación De hopf en una extensión del sistema de lü]]></article-title>
<article-title xml:lang="en"><![CDATA[Analytical treatment of the hopf Bifurcation in an extension of the lü system]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Calderón-Saavedra]]></surname>
<given-names><![CDATA[Pablo Emilio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Muñoz-Aguirre]]></surname>
<given-names><![CDATA[Evodio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Alvarez-Mena]]></surname>
<given-names><![CDATA[Jorge]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Tolima Facultad de Ciencias ]]></institution>
<addr-line><![CDATA[ Ibagué]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Veracruzana Facultad de Matemáticas ]]></institution>
<addr-line><![CDATA[ Xalapa]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Misma dirección que  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>25</volume>
<numero>1</numero>
<fpage>29</fpage>
<lpage>40</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332018000100029&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332018000100029&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332018000100029&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen 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.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract 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.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[sistema tipo Lorenz]]></kwd>
<kwd lng="es"><![CDATA[teorema de la variedad central]]></kwd>
<kwd lng="es"><![CDATA[teorema de la bifurcación de Hopf]]></kwd>
<kwd lng="en"><![CDATA[Lorenz-type systems]]></kwd>
<kwd lng="en"><![CDATA[center manifold theorem]]></kwd>
<kwd lng="en"><![CDATA[Hopf bifurcation theorem]]></kwd>
</kwd-group>
</article-meta>
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