<?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>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2020000400440</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.66.440</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[On the Lagrangians and potentials of a two coupled damped Duffing oscillators system and their application on three-node motif networks]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Barba-Franco]]></surname>
<given-names><![CDATA[J. J.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Espinoza]]></surname>
<given-names><![CDATA[P. B.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gallegos]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Jaimes-Reátegui]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Macías-Díaz]]></surname>
<given-names><![CDATA[J.E.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Guadalajara Centro Universitario de los Lagos Departamento de Ciencias Exactas y Tecnología]]></institution>
<addr-line><![CDATA[Lagos de Moreno Jal.]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma de Aguascalientes Departamento de Matemáticas y Física ]]></institution>
<addr-line><![CDATA[Aguascalientes Ags.]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>08</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>08</month>
<year>2020</year>
</pub-date>
<volume>66</volume>
<numero>4</numero>
<fpage>440</fpage>
<lpage>445</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2020000400440&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2020000400440&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2020000400440&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this work, we investigate the Lagrangians and potentials for two coupled damped Duffing oscillators both directionally and bi-directionally. We show that, although it is not always possible to define a potential in dissipative systems, the potential of our model can be defined if the damping coefficient has a logarithmic derivative form. It is possible to apply these results to the analysis of the dynamics of complex networks based on three-node motif configurations. As an example, we study numerically the dynamics for one of the thirteen different possible configurations. Here, the phenomenon of synchronization is observed in terms of the coupling parameter.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Duffing oscillator]]></kwd>
<kwd lng="en"><![CDATA[motif network]]></kwd>
<kwd lng="en"><![CDATA[Lagrangian]]></kwd>
<kwd lng="en"><![CDATA[coupled oscillators]]></kwd>
<kwd lng="en"><![CDATA[damped systems]]></kwd>
</kwd-group>
</article-meta>
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