Document Zbl 1465.92136

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Franklin Inst.</a> <a href="/?q=in%3A464248" title="Articles in this Issue">358, No. 9, 4883-4894 (2021)</a>. </div> <div class="abstract">Summary: This paper proposes a systematic approach to analyze the stability of a food chain system with a free delay parameter $\tau$ and a free system parameter $\zeta$. Our objective is to study the stability in the whole $\zeta$-$\tau$ plane. First, we consider the case when $\zeta$ is fixed and analyze the stability along the whole $\tau$ axis. Such a problem, called the complete stability problem w.r.t. delay, can be solved through addressing the corresponding auxiliary characteristic roots. Next, we proceed to consider the case when $\zeta$ is also a free parameter. We will obtain the complete classification for the auxiliary characteristic roots. As a result, we can characterize the stability property (more precisely, we can determine the possible number of stability $\tau $-intervals and analytically calculate them) over the whole $\zeta$-$\tau$ plane. The methodology presented in this paper offers a new way to design $\zeta$, with the associated stability $\tau $-intervals explicitly available. Finally, a numerical example is given to illustrate our methodology. It is interesting to see that, for some values of $\zeta$ the system may have many stability $\tau$-intervals, and all such values can be identified by our methodology.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7356369">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%3A92D40" title="MSC2020">92D40</a> </td> <td class="space"> Ecology </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D05" title="MSC2020">93D05</a> </td> <td class="space"> Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.) in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afood+chain+system">food chain system</a>; <a href="/?q=ut%3Afree+delay+parameter">free delay parameter</a>; <a href="/?q=ut%3Acomplete+stability">complete stability</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 1465.92136" data-ciurl="/ci/07356369" data-biburl="/bibtex/07356369.bib" data-amsurl="/amsrefs/07356369.bib" data-xmlurl="/xml/07356369.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07356369.pdf" title="Zbl 1465.92136 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.jfranklin.2021.04.003" aria-label="DOI for “Stability analysis of delayed food chain systems with heterogeneous free parameters”" title="10.1016/j.jfranklin.2021.04.003">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">May, R. 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