Document Zbl 1460.92129

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Math. Biol.</a> <a href="/?q=in%3A458568" title="Articles in this Issue">83, No. 1, Paper No. 4, 17 p. (2021)</a>. </div> <div class="abstract">Summary: Based on the fact that the continuous culture of microorganisms in a chemostat is subject to environmental noises, we present and analyze a stochastic competition chemostat model with general monotonic response functions and differential removal rates. The existence and boundedness of the unique positive solution are first obtained. By defining a stochastic break-even concentration for every species, we prove that at most one competitor survives in the chemostat and the winner has the smallest stochastic break-even concentration, provided its response function satisfies a technical assumption. That is to say, the competitive exclusion principle holds for the stochastic competition chemostat model. Furthermore, we find that the noise experienced by one species is adverse to its growth while may be favorable for the growth of other one species. Namely, the destinies can be exchanged between two microorganism species in the chemostat due to the environmental noise.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7328493">Cited in <strong>27</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A92C75" title="MSC2020">92C75</a> </td> <td class="space"> Biotechnology </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60H30" title="MSC2020">60H30</a> </td> <td class="space"> Applications of stochastic analysis (to PDEs, etc.) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Astochastic+chemostat+model">stochastic chemostat model</a>; <a href="/?q=ut%3Ageneral+response+function">general response function</a>; <a href="/?q=ut%3Astochastic+break-even+concentration">stochastic break-even concentration</a>; <a href="/?q=ut%3Acompetitive+exclusion+principle">competitive exclusion principle</a>; <a href="/?q=ut%3Anoise-induced+conversion+of+species%27+destinies">noise-induced conversion of species’ destinies</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 1460.92129" data-ciurl="/ci/07328493" data-biburl="/bibtex/07328493.bib" data-amsurl="/amsrefs/07328493.bib" data-xmlurl="/xml/07328493.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07328493.pdf" title="Zbl 1460.92129 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/10.1007/s11538-020-00843-7" aria-label="DOI for “Competitive exclusion in a general multi-species chemostat model with stochastic perturbations”" title="10.1007/s11538-020-00843-7">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">Beddington, JR; 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