<?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>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2022000100025</article-id>
<article-id pub-id-type="doi">10.18273/revint.v40n1-2022002</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[The multi-patch logistic equation with asymmetric migration]]></article-title>
<article-title xml:lang="es"><![CDATA[La ecuación logística de múltiples sitios con migración asimétrica]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Elbetch]]></surname>
<given-names><![CDATA[Bilel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Benzekri]]></surname>
<given-names><![CDATA[Tounsia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Massart]]></surname>
<given-names><![CDATA[Daniel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sari]]></surname>
<given-names><![CDATA[Tewfik]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,University Dr. Moulay Tahar of Saida Department of Mathematics ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Algeria</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Department of Mathematics  ]]></institution>
<addr-line><![CDATA[Algiers ]]></addr-line>
<country>Algeria</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Univ Montpellier  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>France</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Univ Montpellier  ]]></institution>
<addr-line><![CDATA[Montpellier ]]></addr-line>
<country>France</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>40</volume>
<numero>1</numero>
<fpage>25</fpage>
<lpage>57</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2022000100025&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2022000100025&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2022000100025&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. This paper is a follow-up to a previous work where we considered a multi-patch model, each patch following a logistic law, the patches being coupled by symmetric migration terms. In this paper we drop the symmetry hypothesis. First, in the case of perfect mixing, i.e when the migration rate tends to infinity, the total population follows a logistic law with a carrying capacity which in general is different from the sum of the n carrying capacities, and depends on the migration terms. Second, we determine, in some particular cases, the conditions under which fragmentation and asymmetrical migration can lead to a total equilibrium population greater or smaller than the sum of the carrying capacities. Finally, for the three-patch model, we show numerically the existence of at least three critical values of the migra-tion rate for which the total equilibrium population equals the sum of the carrying capacities.  MSC2010:  37N25, 92D25, 34D23, 34D15.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. Este artículo es un seguimiento de un trabajo anterior, donde consideramos un modelo de múltiples parches, cada parche siguiendo una ley logística, los sitios estando relacionados por términos de migración simétrica. En este artículo eliminamos la hipótesis de simetría. Primero, en el caso de una mezcla perfecta, es decir, cuando la tasa de migración tiende al infinito, la población total sigue una ley logística con una capacidad de carga que en general es diferente de la suma de las capacidades de carga de los sitios, y depende de los términos de migración. En segundo lugar, determinamos, en algunos casos particulares, las condiciones bajo las cuales la fragmentación y la migración asimétrica pueden llevar a una población total de equilibrio mayor o menor que la suma de las capacidades de carga. Finalmente, para el modelo de tres sitios, mostramos numéricamente la existencia de al menos tres valores críticos de la tasa de migración para los cuales la población total de equilibrio es igual a la suma de las capacidades de carga.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Population dynamics]]></kwd>
<kwd lng="en"><![CDATA[asymmetrical migration]]></kwd>
<kwd lng="en"><![CDATA[logistic equation]]></kwd>
<kwd lng="en"><![CDATA[slow-fast systems]]></kwd>
<kwd lng="en"><![CDATA[perfect mixing]]></kwd>
<kwd lng="es"><![CDATA[Dinámica de población]]></kwd>
<kwd lng="es"><![CDATA[migración asimétrica]]></kwd>
<kwd lng="es"><![CDATA[ecuación logís-tica]]></kwd>
<kwd lng="es"><![CDATA[sistemas lentos y rápidos]]></kwd>
<kwd lng="es"><![CDATA[mezcla perfecta]]></kwd>
</kwd-group>
</article-meta>
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