Document Zbl 1473.92026

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Nonlinear Sci. Numer. Simul.</a> <a href="/?q=in%3A452997" title="Articles in this Issue">37, 1-13 (2016)</a>. </div> <div class="abstract">Summary: A stochastic chemostat model with periodic washout rate is proposed in this paper. First, sufficient conditions are established for the existence of stochastic nontrivial positive periodic solution for the system, on the basis of Khasminskii’s theory for periodic Markov processes. Furthermore, we observe that there exists a unique boundary periodic solution of the stochastic model which is globally attractive. Numerical simulations are carried out to illustrate our main conclusions.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7247587">Cited in <strong>32</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A92C99" title="MSC2020">92C99</a> </td> <td class="space"> Physiological, cellular and medical topics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34C25" title="MSC2020">34C25</a> </td> <td class="space"> Periodic solutions to ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34F05" title="MSC2020">34F05</a> </td> <td class="space"> Ordinary differential equations and systems with randomness </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Achemostat+model">chemostat model</a>; <a href="/?q=ut%3Amonod+response+function">monod response function</a>; <a href="/?q=ut%3Aperiodic+washout+rate">periodic washout rate</a>; <a href="/?q=ut%3Aperiodic+Markov+process">periodic Markov process</a>; <a href="/?q=ut%3Aperiodic+solution">periodic solution</a>; <a href="/?q=ut%3Aglobally+attractive">globally attractive</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 1473.92026" data-ciurl="/ci/07247587" data-biburl="/bibtex/07247587.bib" data-amsurl="/amsrefs/07247587.bib" data-xmlurl="/xml/07247587.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07247587.pdf" title="Zbl 1473.92026 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/10.1016/j.cnsns.2016.01.002" aria-label="DOI for “The periodic solutions of a stochastic chemostat model with periodic washout rate”" title="10.1016/j.cnsns.2016.01.002">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">Monod, J., La technique de la culture continue, theorie et applications, Annales de I’Institut Pasteur, 79, 390-410 (1950)</td> </tr><tr> <td>[2]</td> <td class="space">Novick, A.; Szilard, L., Description of the chemostat, Science, 112, 715-716 (1950)</td> </tr><tr> <td>[3]</td> <td class="space">Smith, HL.; Waltman, P., The theory of the chemostat: dynamics of microbial competition (1995), Cambridge University Press: Cambridge University Press Cambridge · <a href="/0860.92031" class="nowrap">Zbl 0860.92031</a></td> </tr><tr> <td>[4]</td> <td class="space">Chen, L.; Chen, J., Nonlinear biological dynamical system (1993), Science Press: Science Press Beijing</td> </tr><tr> <td>[5]</td> <td class="space">Stewart, FM.; Levin, BR., Partitioning of resources and the outcome of interspecific competition: a model and some general considerations, Am Nat, 107, 171-198 (1973)</td> </tr><tr> <td>[6]</td> <td class="space">Hsu, SB.; Hubbell, S.; Waltman, P., A mathematical theory for single-nutrient competition in continuous cultures of micro-organism, SIAM J Appl Math, 32, 366-383 (1977) · <a href="/0354.92033" class="nowrap">Zbl 0354.92033</a></td> </tr><tr> <td>[7]</td> <td class="space">Gard, TC., A new liapunov function for the simple chemostat, Nonlin. 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