<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00846559</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-24T15:55:33+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Emergence and Propagation of Patterns in Nonlocal Reaction-Diffusion Equations Arising in the Theory of Speciation.</title>
            <author role="aut">
              <persName>
                <forename type="first">Vitaly</forename>
                <surname>Volpert</surname>
              </persName>
              <email type="md5">6e77591b4ba5dab20c532163d80eee55</email>
              <email type="domain">math.univ-lyon1.fr</email>
              <idno type="idhal" notation="numeric">858172</idno>
              <idno type="halauthorid" notation="string">121416-858172</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-5323-9934</idno>
              <affiliation ref="#struct-108959"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Vitali</forename>
                <surname>Vougalter</surname>
              </persName>
              <idno type="halauthorid">222986-0</idno>
              <affiliation ref="#struct-146329"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Vitaly</forename>
                <surname>Volpert</surname>
              </persName>
              <email type="md5">6e77591b4ba5dab20c532163d80eee55</email>
              <email type="domain">math.univ-lyon1.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2013-07-19 12:59:43</date>
              <date type="whenWritten">2013</date>
              <date type="whenModified">2026-04-23 14:50:04</date>
              <date type="whenReleased">2013-07-19 12:59:43</date>
              <date type="whenProduced">2013-07-19</date>
              <ref type="externalLink" target="https://api.istex.fr/ark:/67375/HCB-Q2280K69-W/fulltext.pdf?sid=hal"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="103525">
                <persName>
                  <forename>Vitaly</forename>
                  <surname>Volpert</surname>
                </persName>
                <email type="md5">6e77591b4ba5dab20c532163d80eee55</email>
                <email type="domain">math.univ-lyon1.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00846559</idno>
            <idno type="halUri">https://hal.science/hal-00846559</idno>
            <idno type="halBibtex">volpert:hal-00846559</idno>
            <idno type="halRefHtml">&lt;i&gt;Dispersal, Individual Movement and Spatial Ecology&lt;/i&gt;, Springer-Verlag, pp.331-353, 2013, Lecture Notes in Mathematics, 978-3-642-35497-7. &lt;a target="_blank" href="https://dx.doi.org/10.1007/978-3-642-35497-7_12"&gt;&amp;#x27E8;10.1007/978-3-642-35497-7_12&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Dispersal, Individual Movement and Spatial Ecology, Springer-Verlag, pp.331-353, 2013, Lecture Notes in Mathematics, 978-3-642-35497-7. &amp;#x27E8;10.1007/978-3-642-35497-7_12&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-ST-ETIENNE">Université Jean Monnet - Saint-Etienne</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="ICJ" corresp="UNIV-LYON1">Institut Camille Jordan</idno>
            <idno type="stamp" n="UNIV-LYON1">Université Claude Bernard - Lyon I</idno>
            <idno type="stamp" n="INSA-LYON">Institut National des Sciences Appliquées de Lyon</idno>
            <idno type="stamp" n="EC-LYON">Ecole Centrale de Lyon</idno>
            <idno type="stamp" n="INRIA-RHA">INRIA Grenoble - Rhône-Alpes</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="CGPHIMC">Centre de génétique et de physiologie moléculaire et céllulaire</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="INRIA-RENGRE">INRIA-RENGRE</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="UDL">UDL</idno>
            <idno type="stamp" n="UNIV-LYON">Université de Lyon</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Emergence and Propagation of Patterns in Nonlocal Reaction-Diffusion Equations Arising in the Theory of Speciation.</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Vitaly</forename>
                    <surname>Volpert</surname>
                  </persName>
                  <email type="md5">6e77591b4ba5dab20c532163d80eee55</email>
                  <email type="domain">math.univ-lyon1.fr</email>
                  <idno type="idhal" notation="numeric">858172</idno>
                  <idno type="halauthorid" notation="string">121416-858172</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-5323-9934</idno>
                  <affiliation ref="#struct-108959"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Vitali</forename>
                    <surname>Vougalter</surname>
                  </persName>
                  <idno type="halauthorid">222986-0</idno>
                  <affiliation ref="#struct-146329"/>
                </author>
              </analytic>
              <monogr>
                <idno type="isbn">978-3-642-35497-7</idno>
                <title level="m">Dispersal, Individual Movement and Spatial Ecology</title>
                <imprint>
                  <publisher>Springer-Verlag</publisher>
                  <biblScope unit="serie">Lecture Notes in Mathematics</biblScope>
                  <biblScope unit="pp">331-353</biblScope>
                  <date type="datePub">2013-07-19</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1007/978-3-642-35497-7_12</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halTypology" n="COUV">Book sections</classCode>
              <classCode scheme="halOldTypology" n="COUV">Book sections</classCode>
              <classCode scheme="halTreeTypology" n="COUV">Book sections</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Emergence and propagation of patterns in population dynamics is related to the process of speciation, appearance of new biological species. This process will be studied with a nonlocal reaction-diffusion equation where the integral term describes nonlocal consumption of resources. This equation can have several stationary points and, as it is already well known, a travelling wave solution which provides a transition between them. It is also possible that one of these stationary points loses its stability resulting in appearance of a stationary periodic in space structure. In this case, we can expect a possible transition between a stationary point and a periodic structure. The main goal of this work is to study such transitions. The loss of stability of the stationary point signifies that the essential spectrum of the operator linearized about the wave intersects the imaginary axis. Contrary to the usual Hopf bifurcation where a pair of isolated complex conjugate eigenvalues crosses the imaginary axis, here a periodic solution may not necessarily emerge. To describe dynamics of solutions, we need to consider two transitions: a steady wave with a constant speed between two stationary points, and a periodic wave between the stationary point which loses its stability and the periodic structure which appears around it. Both of these waves propagate in space, each one with its own speed. If the speed of the steady wave is greater, then it runs away from the periodic wave, and they propagate independently one after another.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-108959" status="OLD">
          <idno type="RNSR">201020961V</idno>
          <orgName>Multi-scale modelling of cell dynamics : application to hematopoiesis</orgName>
          <orgName type="acronym">DRACULA</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>Institut Camille Jordan Université Claude Bernard Lyon 1 43 boulevard du 11 novembre 1918 69622 Villeurbanne cedex France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/dracula</ref>
          </desc>
          <listRelation>
            <relation active="#struct-711" type="direct"/>
            <relation active="#struct-194495" type="indirect"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation name="UMR5534" active="#struct-441569" type="indirect"/>
            <relation active="#struct-2497" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-193738" type="direct"/>
            <relation active="#struct-126765" type="indirect"/>
            <relation active="#struct-219748" type="indirect"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-300284" type="indirect"/>
            <relation active="#struct-1327915" type="indirect"/>
            <relation name="UMR5208" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-146329" status="VALID">
          <orgName>Department of Mathematics and Applied Mathematics [Cape Town]</orgName>
          <desc>
            <address>
              <addrLine>Private Bag Rondebosch 7701 South Africa</addrLine>
              <country key="ZA"/>
            </address>
            <ref type="url">http://www.mth.uct.ac.za/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-303907" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-711" status="OLD">
          <orgName>Centre de génétique et de physiologie moléculaire et cellulaire</orgName>
          <orgName type="acronym">CGPhiMC</orgName>
          <date type="start">1995-01-01</date>
          <date type="end">2015-12-31</date>
          <desc>
            <address>
              <addrLine>bat. 741 43 Bvd du 11 Novembre 1918 69622 VILLEURBANNE CEDEX</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-194495" type="direct"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation name="UMR5534" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-194495" status="VALID">
          <idno type="IdRef">026402823</idno>
          <idno type="ISNI">0000000121686185</idno>
          <idno type="ROR">https://ror.org/029brtt94</idno>
          <orgName>Université Claude Bernard Lyon 1</orgName>
          <orgName type="acronym">UCBL</orgName>
          <desc>
            <address>
              <addrLine>43, boulevard du 11 novembre 1918, 69622 Villeurbanne cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lyon1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301088" status="VALID">
          <idno type="ROR">https://ror.org/01rk35k63</idno>
          <orgName>Université de Lyon</orgName>
          <desc>
            <address>
              <addrLine>92 rue Pasteur - CS 30122, 69361 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-lyon.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-2497" status="VALID">
          <idno type="RNSR">199218244V</idno>
          <idno type="ROR">https://ror.org/00n8d6z93</idno>
          <orgName>Centre Inria de l'Université Grenoble Alpes</orgName>
          <desc>
            <address>
              <addrLine>Inovallée655 avenue de l'Europe38330 Montbonnot</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/grenoble</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-193738" status="VALID">
          <idno type="IdRef">111872227</idno>
          <idno type="ISNI">0000000403832988</idno>
          <idno type="RNSR">200511878U</idno>
          <idno type="ROR">https://ror.org/01ekw7f87</idno>
          <orgName>Institut Camille Jordan</orgName>
          <orgName type="acronym">ICJ</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Bât. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.univ-lyon1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-126765" type="direct"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation active="#struct-194495" type="direct"/>
            <relation active="#struct-219748" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-300284" type="direct"/>
            <relation active="#struct-1327915" type="indirect"/>
            <relation name="UMR5208" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-126765" status="VALID">
          <idno type="ROR">https://ror.org/05s6rge65</idno>
          <orgName>École Centrale de Lyon</orgName>
          <orgName type="acronym">ECL</orgName>
          <desc>
            <address>
              <addrLine>36 avenue Guy de Collongue - 69134 Ecully cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ec-lyon.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-219748" status="VALID">
          <idno type="IdRef">052444724</idno>
          <idno type="ISNI">0000 0001 2292 0228</idno>
          <orgName>Institut National des Sciences Appliquées de Lyon</orgName>
          <orgName type="acronym">INSA Lyon</orgName>
          <date type="start">1957-03-18</date>
          <desc>
            <address>
              <addrLine>20 Avenue Albert Einstein, 69621 Villeurbanne cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-lyon.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
            <relation active="#struct-301232" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300284" status="VALID">
          <idno type="IdRef">028209966</idno>
          <idno type="ISNI">0000 0001 2158 1682</idno>
          <idno type="ROR">https://ror.org/04yznqr36</idno>
          <idno type="Wikidata">Q623154</idno>
          <orgName>Université Jean Monnet - Saint-Étienne</orgName>
          <orgName type="acronym">UJM</orgName>
          <date type="start">1969-03-27</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>10, Rue Tréfilerie – CS 8230142023 Saint-Étienne Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-st-etienne.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-1327915" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-1327915" status="VALID">
          <idno type="IdRef">285395831</idno>
          <orgName>Université Jean Monnet (EPSCPE)</orgName>
          <orgName type="acronym">UJM EPE</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>10 rue Tréfilerie42100 Saint-Etienne</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-st-etienne.fr/fr/index.html</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-303907" status="VALID">
          <idno type="ROR">https://ror.org/03p74gp79</idno>
          <orgName>University of Cape Town</orgName>
          <desc>
            <address>
              <addrLine>Private Bag X3, Rondebosch 7701, South Africa</addrLine>
              <country key="ZA"/>
            </address>
            <ref type="url">https://www.uct.ac.za/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>