Document Zbl 1479.35206

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Under the weak competition condition, the corresponding kinetic system admits a globally stable positive periodic solution $(\hat{u}(t),\hat{v}(t))$. By the method of upper and lower solutions and the Schauder fixed point theorem, we first obtain the existence and nonexistence of traveling wave solutions connecting (0, 0) to $(\hat{u}(t),\hat{v}(t))$. Then we use the comparison arguments to establish the spreading properties for a large class of solutions.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7441040">Cited in <strong>6</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35C07" title="MSC2020">35C07</a> </td> <td class="space"> Traveling wave solutions </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B40" title="MSC2020">35B40</a> </td> <td class="space"> Asymptotic behavior of solutions to PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35K57" title="MSC2020">35K57</a> </td> <td class="space"> Reaction-diffusion equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92D25" title="MSC2020">92D25</a> </td> <td class="space"> Population dynamics (general) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Acompetition+model">competition model</a>; <a href="/?q=ut%3Aspreading+properties">spreading properties</a>; <a href="/?q=ut%3Amethod+of+upper+and+lower+solutions">method of upper and lower solutions</a>; <a href="/?q=ut%3ASchauder+fixed+point+theorem">Schauder fixed point theorem</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1479.35206" data-ciurl="/ci/07441040" data-biburl="/bibtex/07441040.bib" data-amsurl="/amsrefs/07441040.bib" data-xmlurl="/xml/07441040.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07441040.pdf" title="Zbl 1479.35206 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1088/1361-6544/ac37f6" aria-label="DOI for “Traveling waves and spreading properties for a reaction-diffusion competition model with seasonal succession”" title="10.1088/1361-6544/ac37f6">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bao, X.; Wang, Z-C, Existence and stability of time periodic traveling waves for a periodic bistable Lotka-Volterra competition system, J. 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