<?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>S1409-24332022000100053</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v29i1.40956</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Some applications of periodic orbits for competitive systems]]></article-title>
<article-title xml:lang="es"><![CDATA[Algunas aplicaciones de órbitas periódicas a sistemas competitivos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Díaz-Marín]]></surname>
<given-names><![CDATA[Homero G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Osuna]]></surname>
<given-names><![CDATA[Osvaldo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Michoacana Facultad de Ciencias Físico-Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>México</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Michoacana Instituto de Física y Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<volume>29</volume>
<numero>1</numero>
<fpage>53</fpage>
<lpage>68</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332022000100053&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332022000100053&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332022000100053&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We prove existence of periodic orbits for non-autonomous two dimensional competitive dynamical systems with periodic time dependence. The proof is an adaptation of a similar assertion stated for cooperative systems in [ 6 ]. We also give two main applications: one model for cancer cell populations under periodic chemotherapy as treated in [ 4 ] and [ 3 ] for the cooperative case, and another model for mosquito population replacement dynamics interacting with control sterile mosquitoes with periodic release [ 1 ] , for the competitive case.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Probamos la existencia de órbitas periódicas para sistemas dinámicos competitivos en dos dimensiones no autónomos con dependencia periódica respecto al tiempo. La prueba es una adaptación de un resultado similar para sistemas cooperativos en [ 6 ] . También damos dos aplicaciones: un modelo de población de celulas cancerosas sometidas a un tratamiento periódico de quimioterapia como se describe en [ 4 ] y [ 3 ] para el caso cooperativo, y otro modelo de poblaciones de mosquitos interactuando con mosquitos de control estériles liberados periódicamente [ 1 ] , para el caso competitivo.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[competitive systems]]></kwd>
<kwd lng="en"><![CDATA[periodic orbit]]></kwd>
<kwd lng="en"><![CDATA[angiogenesis]]></kwd>
<kwd lng="en"><![CDATA[cancer treatment modeling]]></kwd>
<kwd lng="en"><![CDATA[population replacement modeling]]></kwd>
<kwd lng="en"><![CDATA[Aedes aegypti]]></kwd>
<kwd lng="en"><![CDATA[Wolbachia.]]></kwd>
<kwd lng="es"><![CDATA[sistemas competitivos]]></kwd>
<kwd lng="es"><![CDATA[órbita periódica]]></kwd>
<kwd lng="es"><![CDATA[angiogénesis]]></kwd>
<kwd lng="es"><![CDATA[modelado de tratamientos de cáncer]]></kwd>
<kwd lng="es"><![CDATA[modelo de reemplazo de población]]></kwd>
<kwd lng="es"><![CDATA[Aedes aegypti]]></kwd>
<kwd lng="es"><![CDATA[Wolbachia.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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