<?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>0121-7488</journal-id>
<journal-title><![CDATA[Ciencia en Desarrollo]]></journal-title>
<abbrev-journal-title><![CDATA[Ciencia en Desarrollo]]></abbrev-journal-title>
<issn>0121-7488</issn>
<publisher>
<publisher-name><![CDATA[Universidad Pedagógica y Tecnológica de Colombia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-74882018000100063</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Bifurcación de Hopf en un modelo de desarrollo sostenible]]></article-title>
<article-title xml:lang="en"><![CDATA[Hopf bifurcation in a model of sustainable development]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Granada D]]></surname>
<given-names><![CDATA[H.A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ángel G]]></surname>
<given-names><![CDATA[M.A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Moreno O]]></surname>
<given-names><![CDATA[D.K.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Canchila M]]></surname>
<given-names><![CDATA[J.A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Tolima Facultad de Ciencias Departamento de Matemáticas y Estadística]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad del Tolima Facultad de Ciencias Departamento de Matemáticas y Estadística]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad del Tolima Facultad de Ciencias Departamento de Matemáticas y Estadística]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad Nacional de Colombia Facultad de Ciencias Exactas y Naturales Departamento de Matemáticas y Estadística]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</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>9</volume>
<numero>1</numero>
<fpage>63</fpage>
<lpage>70</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-74882018000100063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-74882018000100063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-74882018000100063&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Se presenta un sistema conformado por tres ecuaciones diferenciales ordinarias de primer orden que permiten estudiar la interacción dinámica entre los recursos renovables, la población y la contaminación ambiental de una región. El modelo se obtiene acoplando una ecuación dinámica de contaminación al sistema formulado por Simone D'alessandro y se muestra que bajo la bifurcación de Hopf se puede alcanzar el desarrollo sostenible bajo la definición dada en el informe de Brundtland 1987. Es decir, cuando se alcanza un balance armónico entre las variables de estado del modelo.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This article presents a system of three first-orden ordinary differential equations to study the dynamic interaction between renewable resources, population and environmental pollution in a region. The model is achieved coupling a dynamic equation of contamination to formulated systems by Simone D'alessandro and shows that under the Hopf bifurcation can be found conditions to achieve sustainable development under the definition given in the report of Brundtland commission 1987. That is, when a harmonic balance between the state variables of the model is reached.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Sistemas dinámicos]]></kwd>
<kwd lng="es"><![CDATA[dinámica no lineal]]></kwd>
<kwd lng="es"><![CDATA[bifurcación de Hopf]]></kwd>
<kwd lng="es"><![CDATA[desarrollo sostenible]]></kwd>
<kwd lng="es"><![CDATA[huella ecológica]]></kwd>
<kwd lng="en"><![CDATA[Dynamical systems]]></kwd>
<kwd lng="en"><![CDATA[nonlinear dynamics]]></kwd>
<kwd lng="en"><![CDATA[Hopf bifurcation]]></kwd>
<kwd lng="en"><![CDATA[sustainable development]]></kwd>
<kwd lng="en"><![CDATA[ecological footprint]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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