<?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>0121-1935</journal-id>
<journal-title><![CDATA[Revista de Ciencias]]></journal-title>
<abbrev-journal-title><![CDATA[rev. cienc.]]></abbrev-journal-title>
<issn>0121-1935</issn>
<publisher>
<publisher-name><![CDATA[Universidad del Valle]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-19352017000200059</article-id>
<article-id pub-id-type="doi">10.25100/rc.v21i2.6699</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Identificación de una bifurcación de Hopf con o sin parámetros]]></article-title>
<article-title xml:lang="en"><![CDATA[Identification of a Hopf bifurcation with or without parameters]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cortés García]]></surname>
<given-names><![CDATA[Christian Camilo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Surcolombiana Departamento de Matemática y Estadística ]]></institution>
<addr-line><![CDATA[Neiva ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<volume>21</volume>
<numero>2</numero>
<fpage>59</fpage>
<lpage>82</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-19352017000200059&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-19352017000200059&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-19352017000200059&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este trabajo se presenta los lineamientos teóricos que identifica la existencia de una bifurcación genérica de Hopf, con o sin parámetros, a través de un punto o una línea de puntos de equilibrio para un sistema dinámico continúo. Con estos lineamientos definidos, se analiza la bifurcación de Hopf sin parámetros a través del estudio de contornos viscosos para un sistema de ecuaciones diferenciales parciales conformado por un término de reacción - difusión; con condición inicial constante a trozos y una línea de puntos de equilibrio que presenta un par de valores propios complejos conjugados con parte real nula en su linealización a medida que se aproxima al origen. En condiciones adecuadas, se distinguen dos casos para este tipo de bifurcación genérica de Hopf sin parámetros: hiperbólica y elíptica, genéricas en el sentido que es una bifurcación controlada en una línea de puntos de equilibrio.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper, we present the theoretical guidelines that identify the presence of a generic Hopf bifurcation, with or without parameters, through a point or a line of equilibrium points for a continuous dynamic system. With these defined guidelines, the Hopf bifurcation without parameters is analyzed through the study of viscous contours for a system of partial differential equations conformed by a reaction-diffusion term; with initial condition constant to pieces and a line of equilibrium points that presents a pair of complex eigenvalues conjugated with null real part in its linearization as it approaches the origin. Under appropriate conditions, two cases are distinguished for this type of generic Hopf bifurcation without parameters: hyperbolic and elliptical, generic in the sense that it is a controlled bifurcation in a line of equilibrium points.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[viscous profiles]]></kwd>
<kwd lng="en"><![CDATA[hyperbolic system of conservation laws]]></kwd>
<kwd lng="en"><![CDATA[Riemann problem]]></kwd>
<kwd lng="en"><![CDATA[equilibrium line]]></kwd>
<kwd lng="es"><![CDATA[contornos viscosos]]></kwd>
<kwd lng="es"><![CDATA[sistema hiperbólico con leyes de conservación]]></kwd>
<kwd lng="es"><![CDATA[problema de Riemman]]></kwd>
<kwd lng="es"><![CDATA[línea de equilibrio]]></kwd>
</kwd-group>
</article-meta>
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