<?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>S1409-24332016000200489</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Análisis de un modelo planta-herbívoro aplicado a la interacción gramínea-bovino]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[RomeroL.]]></surname>
<given-names><![CDATA[JhoanaP.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ibargüen]]></surname>
<given-names><![CDATA[Eduardo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pulgarín]]></surname>
<given-names><![CDATA[Alejandra]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cordero]]></surname>
<given-names><![CDATA[Deyber]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Castaño]]></surname>
<given-names><![CDATA[IngridP.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Antioquia  ]]></institution>
<addr-line><![CDATA[ Medellín]]></addr-line>
<country>CO</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Nariño Facultad de Ciencias ]]></institution>
<addr-line><![CDATA[ Pasto]]></addr-line>
<country>CO</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad del Quindío Facultad de Ciencias Básicas ]]></institution>
<addr-line><![CDATA[ Armenia]]></addr-line>
<country>CO</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de Antioquia Facultad de Ciencias Agrarias ]]></institution>
<addr-line><![CDATA[ Medellín]]></addr-line>
<country>CO</country>
</aff>
<aff id="Af5">
<institution><![CDATA[,Universidad de Antioquia Facultad de Ciencias Agrarias ]]></institution>
<addr-line><![CDATA[ Medellín]]></addr-line>
<country>CO</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<volume>23</volume>
<numero>2</numero>
<fpage>489</fpage>
<lpage>506</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332016000200489&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332016000200489&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332016000200489&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenEn este trabajo se describe una dinámica de interacción interespecífica gramínea-bovino a través de un modelo presa-predador con una respuesta funcional Holling tipo II. El análisis cualitativo revela la existencia de una bifurcación de Hopf supercrítica con parámetro de bifurcación decreciente que se correlaciona con tres equilibrios: uno inestable donde no existen especies, otro con solo gramínea y uno donde coexisten ambas especies. Estos resultados, validados con datos estadísticos de investigaciones realizadas en la región Caribe y valles interandinos de Colombia, muestran la relevancia de un consumo de gramínea sostenible por parte de los bovinos.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractIn this work we describe an interspecific interaction dynamics between grass and bovines through a predator-prey model with a functional response of Holling tipe II. Qualitative analysis reveals the existence of a supercritical Hopf bifurcation with decreasing bifurcation parameter correlated with three equilibrium solutions: the trivial equilibrium without species, the equilibrium only with grass and the equilibrium of coexistence between the both species. These results were validated with statistical data from research conducted in the Caribbean region and interandinos valleys of Colombia. They show the relevance of grass sustainable consumption by bovines.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[gramínea]]></kwd>
<kwd lng="es"><![CDATA[bovinos]]></kwd>
<kwd lng="es"><![CDATA[bifurcación de Hopf]]></kwd>
<kwd lng="es"><![CDATA[modelo presa-predador]]></kwd>
<kwd lng="en"><![CDATA[grass]]></kwd>
<kwd lng="en"><![CDATA[bovines]]></kwd>
<kwd lng="en"><![CDATA[Hopf bifurcation]]></kwd>
<kwd lng="en"><![CDATA[prey-predator model]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[A model for a forested grassland: effect or overgrazing and pollution]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Agarwal]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Mishra]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<source><![CDATA[Indian Journal of Pure and Applied Mathematics]]></source>
<year>2001</year>
<volume>32</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>613-28</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Baca Carrasco]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Análisis Paramétrico de la Bifurcación de Hopf en Sistemas Tipo Lorenz]]></source>
<year>2007</year>
<publisher-loc><![CDATA[Sonora, México ]]></publisher-loc>
<publisher-name><![CDATA[Universidad de Sonora]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cuesta-Muñoz]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Mateus Echavarria]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Santana]]></surname>
<given-names><![CDATA[R.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Barro Henríquez]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Estrategias de manejo de praderas para mejorar la productividad de la ganadería en las regiones Caribe y Valles Interandinos]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Cuesta]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Producción y Utilización de Recursos Forrajeros en Sistemas de Producción Bovina en el Caribe y Valles Interandinos]]></source>
<year>2006</year>
<page-range>43-64</page-range><publisher-name><![CDATA[Corporación Colombiana de Investigación Agropecuaria (Corpoica)]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Farkas]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Dynamical Models in Biology]]></source>
<year>2001</year>
<publisher-loc><![CDATA[San Diego CA. ]]></publisher-loc>
<publisher-name><![CDATA[Academic Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[La respuesta funcional: una revisión y guía experimental]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Corley]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ecología Austral]]></source>
<year>2004</year>
<volume>14</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>83-93</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Es constante el patrón espacial y temporal de la interacción árbol-pasto en dehesas]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gea Izquierdo]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Cañellas Rey de Viñas]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Montero González]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Cuad. Soc. Esp. Cienc. For]]></source>
<year>2007</year>
<volume>22</volume>
<page-range>45-50</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ko]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Ryu]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Differential Equations]]></source>
<year>2006</year>
<volume>231</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>534-50</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kuznetsov]]></surname>
<given-names><![CDATA[Y.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Elements of Applied Bifurcation Theory]]></source>
<year>1998</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lafaurie]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Logros, Legados y Derroteros 2011-2012]]></source>
<year>2012</year>
<publisher-loc><![CDATA[Bogotá ]]></publisher-loc>
<publisher-name><![CDATA[FEDEGANFondo Nacional del Ganado]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Permanence for a delayed discrete ratio-dependent N-species predator-prey system with Holling-type II functional response]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Liu]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Gao]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical and Computer Modelling]]></source>
<year>2010</year>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Situación actual de la ganadería de carne en Colombia y alternativas para impulsar su competitividad y sostenibilidad]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mahecha]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Gallego]]></surname>
<given-names><![CDATA[L.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Peláez]]></surname>
<given-names><![CDATA[F.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Revista Colombiana de Ciencias Pecuarias]]></source>
<year>2002</year>
<volume>15</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>213-25</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Determinación de la capacidad de carga y ganancia de peso de bovinos en pastoreo de gramíneas nativas en Piedemonte amazónico de Colombia]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Maldonado]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Velásquez]]></surname>
<given-names><![CDATA[J.E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Pasturas Tropicales]]></source>
<year>1994</year>
<volume>16</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>2-8</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mandujano]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ecología de Poblaciones Aplicada al Manejo de Fauna Silvestre]]></source>
<year>2011</year>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Instituto Literario de Veracruz S.C.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[V.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Estudio de la Desertificación por Sobrepastoreo Mediante un Modelo de Simulación Dinámica]]></source>
<year>2005</year>
<publisher-loc><![CDATA[Madrid, España ]]></publisher-loc>
<publisher-name><![CDATA[Universidad Politécnica de Madrid]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Onoff policy and hysteresis on-off policy control of the herbivore-vegetation dynamics in a semi-arid grazing system]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mendoza]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Bhaya]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Kaszkurewicz]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Da Silveira]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ecological Engineering]]></source>
<year>2006</year>
<volume>28</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>114-23</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Moreno-Osorio]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Molina Restrepo]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Manual Técnico: Buenas Prácticas Agropecuarias en la Producción de Ganado de Doble Propósito Bajo Confinamiento, con Caña Panelera Como Parte de la Dieta]]></source>
<year>2007</year>
<publisher-loc><![CDATA[Medellín, Colombia ]]></publisher-loc>
<publisher-name><![CDATA[CORPOICA]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Perko]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Differential Equations and Dynamical Systems]]></source>
<year>1996</year>
<edition>Second</edition>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rincón]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ceba de bovinos en pasturas de Bracharia decumbens suplementados con caña de azúcar y Cratylia argente]]></article-title>
<collab>Tropical Forages</collab>
<source><![CDATA[Pasturas Tropicales]]></source>
<year>2005</year>
<volume>27</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>2-12</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Valverde]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Cano]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ecología y Medio Ambiente]]></source>
<year>2009</year>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Pearson Educación]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zamora]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Las interacciones planta-planta y planta-animal en el contexto de la sucesión ecológica]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Valladares]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ecología del Bosque Mediterráneo en un Mundo Cambiante]]></source>
<year>2004</year>
<page-range>371-93</page-range><publisher-loc><![CDATA[Madrid, España ]]></publisher-loc>
<publisher-name><![CDATA[Ministerio de Medio Ambiente]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Positive steady state solutions of a Leslie-Gower predatorprey model with Holling type II functional response and density-dependent diffusion]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zhou]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Nonlinear Analysis: Theory, Methods y Applications]]></source>
<year>2013</year>
<volume>82</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>47-65</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
