Document Zbl 1519.92131

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Biol. Syst.</a> <a href="/?q=in%3A499866" title="Articles in this Issue">31, No. 2, 643-672 (2023)</a>. </div> <div class="abstract">Summary: In this paper, we consider a stochastic food chain chemostat model with variable yields. First, we prove the stochastic model has a unique global positive solution. Second, by employing suitable Lyapunov functions, Itô’s formula and some other important inequalities, the existence of a unique ergodic stationary distribution of a stochastic food chain chemostat model is researched, which can help us better understand the statistical characteristics of stochastic food chain chemostat models. Second, we investigate the extinction of the microorganism and the bacteria. Moreover, the case of extinction for bacteria but persistence for microbial species is considered. Finally, some numerical simulations are carried out to illustrate our theoretical results and the influence of the variable yields on the microorganism and the bacteria.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7715361">Cited in <strong>1</strong> Document</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%3A92D40" title="MSC2020">92D40</a> </td> <td class="space"> Ecology </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q92" title="MSC2020">35Q92</a> </td> <td class="space"> PDEs in connection with biology, chemistry and other natural sciences </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60G10" title="MSC2020">60G10</a> </td> <td class="space"> Stationary stochastic processes </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Astochastic+food+chain+chemostat+model">stochastic food chain chemostat model</a>; <a href="/?q=ut%3Astochastic+Lyapunov+function">stochastic Lyapunov function</a>; <a href="/?q=ut%3AIt%C3%B4%27s+formula">Itô’s formula</a>; <a href="/?q=ut%3Astationary+distribution">stationary distribution</a>; <a href="/?q=ut%3Aextinction">extinction</a>; <a href="/?q=ut%3Avariable+yield">variable yield</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" 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btn-xs pdf" data-container="body" type="button" href="/pdf/07715361.pdf" title="Zbl 1519.92131 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/10.1142/S0218339023500225" aria-label="DOI for “Dynamical behavior of a stochastic food chain chemostat model with variable yields”" title="10.1142/S0218339023500225">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">Smith, HL, Waltman, P, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, Cambridge, 1995. · <a href="/0860.92031" class="nowrap">Zbl 0860.92031</a></td> </tr><tr> <td>[2]</td> <td class="space">Chen, L, Meng, X, Jiao, J, Biological Dynamics, Science Press, Beijing, 1993.</td> </tr><tr> <td>[3]</td> <td class="space">Fritsch, C, Harmand, J, Campillo, F, A modeling 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