<?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>S0035-001X2016000300267</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Additive and multiplicative noises acting simultaneously on Ermakov-Ray-Reid systems]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cervantes-López]]></surname>
<given-names><![CDATA[E.]]></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[Rosu]]></surname>
<given-names><![CDATA[H.C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Nacional de Estadística y Geografía  ]]></institution>
<addr-line><![CDATA[ Aguascalientes]]></addr-line>
<country>México</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Guadalajara Centro Universitario de los Lagos Departamento de Ciencias Exactas y Tecnología]]></institution>
<addr-line><![CDATA[Lagos de Moreno Jalisco]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Instituto Potosino de Investigación Científica y Tecnológica  ]]></institution>
<addr-line><![CDATA[San Luis Potosí S.L.P.]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<volume>62</volume>
<numero>3</numero>
<fpage>267</fpage>
<lpage>270</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2016000300267&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2016000300267&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2016000300267&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We investigate numerically the effect of additive and multiplicative noises on parametric oscillator systems of Ermakov-Ray-Reid type when both noises act simultaneously. We find that the main perturbation effects on the dynamical invariant of these systems are produced by the additive noise. Different from the separate action of the multiplicative noise when the dynamical invariant of these systems is robust, we also find a weak effect that can be attributed to the multiplicative noise.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Se investigan numéricamente los efectos de los ruidos aditivos y multiplicativos sobre los sistemas dinámicos de osciladores paramétricos de tipo Ermakov-Ray-Reid cuando los dos tipos de ruidos actúan de manera simultánea. La mayor parte de la perturbación del invariante proviene del ruido aditivo. A diferencia del caso cuando el ruido multiplicativo actúa por separado y el invariante dinámico presenta robustez, encontramos que en la acción simultánea de los dos ruidos hay también un efecto pequeño atribuible al ruido multiplicativo.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Noise]]></kwd>
<kwd lng="en"><![CDATA[additive]]></kwd>
<kwd lng="en"><![CDATA[multiplicative]]></kwd>
<kwd lng="en"><![CDATA[Ermakov-Ray-Reid oscillator system]]></kwd>
<kwd lng="en"><![CDATA[dynamical invariant]]></kwd>
<kwd lng="es"><![CDATA[Ruido]]></kwd>
<kwd lng="es"><![CDATA[aditivo]]></kwd>
<kwd lng="es"><![CDATA[multiplicativo]]></kwd>
<kwd lng="es"><![CDATA[sistema oscilante de Ermakov-Ray-Reid]]></kwd>
<kwd lng="es"><![CDATA[invariante dinámico]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Steen]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Overs. over d. K. Danske Vidensk. Selsk. Forh]]></source>
<year>1874</year>
<page-range>1</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ermakov]]></surname>
<given-names><![CDATA[V.P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Univ. Izv. Kiev]]></source>
<year>1880</year>
<volume>20</volume>
<page-range>1</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chini]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Atti Accad. Sci. Torino]]></source>
<year>1898</year>
<volume>33</volume>
<page-range>737</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pinney]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proc. Amer. Math. Soc]]></source>
<year>1950</year>
<volume>1</volume>
<page-range>681</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lewis]]></surname>
<given-names><![CDATA[H.R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Rev. Lett.]]></source>
<year>1967</year>
<volume>18</volume>
<page-range>510</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ray]]></surname>
<given-names><![CDATA[J. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Reid]]></surname>
<given-names><![CDATA[J. L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Lett.]]></source>
<year>1979</year>
<volume>71A</volume>
<page-range>317</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Goncharenko]]></surname>
<given-names><![CDATA[A.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Logvin]]></surname>
<given-names><![CDATA[Y.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Samson]]></surname>
<given-names><![CDATA[A.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Shapovalov]]></surname>
<given-names><![CDATA[P.S.]]></given-names>
</name>
<name>
<surname><![CDATA[Surovets]]></surname>
<given-names><![CDATA[T.I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Lett. A]]></source>
<year>1991</year>
<volume>160</volume>
<page-range>138</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rogers]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Malomed]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Chow]]></surname>
<given-names><![CDATA[K.W.]]></given-names>
</name>
<name>
<surname><![CDATA[An]]></surname>
<given-names><![CDATA[H.L.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Phys. A: Math. Theor.]]></source>
<year>2010</year>
<volume>43</volume>
<page-range>455214</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rogers]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Schief]]></surname>
<given-names><![CDATA[W.K.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Math. Anal. Appl.]]></source>
<year>1996</year>
<volume>198</volume>
<page-range>194</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rogers]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[An]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Stud. Appl. Math.]]></source>
<year>2010</year>
<volume>125</volume>
<page-range>275</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[An]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[An]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Kwong]]></surname>
<given-names><![CDATA[M.K.]]></given-names>
</name>
<name>
<surname><![CDATA[Zhu]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Stud. Appl. Math]]></source>
<year>2016</year>
<volume>136</volume>
<page-range>139</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rogers]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Schief]]></surname>
<given-names><![CDATA[W.K.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Math. Phys.]]></source>
<year>2011</year>
<volume>52</volume>
<page-range>0837101</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schief]]></surname>
<given-names><![CDATA[W.K.]]></given-names>
</name>
<name>
<surname><![CDATA[Rogers]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Bassom]]></surname>
<given-names><![CDATA[A.P.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Phys. A: Math. Gen]]></source>
<year>1996</year>
<volume>29</volume>
<page-range>903</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gitterman]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Noisy Oscillator: The First Hundred Years, From Einstein Until Now]]></source>
<year>2005</year>
<publisher-loc><![CDATA[Singapore ]]></publisher-loc>
<publisher-name><![CDATA[World Scientific]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cervantes-López]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Espinoza]]></surname>
<given-names><![CDATA[P.B.]]></given-names>
</name>
<name>
<surname><![CDATA[Gallegos]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosu]]></surname>
<given-names><![CDATA[H.C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Physica A]]></source>
<year>2014</year>
<volume>401</volume>
<page-range>141</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cervantes-López]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Espinoza]]></surname>
<given-names><![CDATA[P.B.]]></given-names>
</name>
<name>
<surname><![CDATA[Gallegos]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosu]]></surname>
<given-names><![CDATA[H.C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Physica A]]></source>
<year>2015</year>
<volume>439</volume>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ray]]></surname>
<given-names><![CDATA[J.R.]]></given-names>
</name>
<name>
<surname><![CDATA[Reid]]></surname>
<given-names><![CDATA[J.L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Rev. A]]></source>
<year>1982</year>
<volume>26</volume>
<page-range>1042</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gitterman]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Noisy Oscillator: The First Hundred Years, From Einstein Until Now]]></source>
<year>2005</year>
<publisher-loc><![CDATA[Singapore ]]></publisher-loc>
<publisher-name><![CDATA[World Scientific]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Oksendal]]></surname>
<given-names><![CDATA[B.K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Stochastic Differential Equations: An Introduction with Applications]]></source>
<year>2003</year>
<publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Milstein]]></surname>
<given-names><![CDATA[G.N.]]></given-names>
</name>
<name>
<surname><![CDATA[Tretyakov]]></surname>
<given-names><![CDATA[M.V.]]></given-names>
</name>
</person-group>
<source><![CDATA[Stochastic Numerics for Mathematical Physics. Scientific Computation]]></source>
<year>2004</year>
<publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kloeden]]></surname>
<given-names><![CDATA[P.E.]]></given-names>
</name>
<name>
<surname><![CDATA[Platen]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical Solution of Stochastic Differential Equations]]></source>
<year>1992</year>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Oksendal]]></surname>
<given-names><![CDATA[B.K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Stochastic Differential Equations: An Introduction with Applications]]></source>
<year>2003</year>
<page-range>64</page-range><publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
