Document Zbl 1441.93209

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On account of the non-commutativity of quaternion multiplication resulting from Hamilton rules, the FQVNN models are separated into four real-valued neural network (RVNN) models. Consequently, the dynamic analysis of FQVNNs can be realized by investigating the real-valued ones. Based on the method of $M$-matrix, the existence and uniqueness of the equilibrium point of the FQVNNs are obtained without detailed proof. Afterwards, several sufficient criteria ensuring the global Mittag-Leffler stability for the unique equilibrium point of the FQVNNs are derived by applying the Lyapunov direct method, the theory of fractional differential equation, the theory of matrix eigenvalue, and some inequality techniques. In the meanwhile, global Mittag-Leffler synchronization for the drive-response models of the addressed FQVNNs are investigated explicitly. Finally, simulation examples are designed to verify the feasibility and availability of the theoretical results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7201443">Cited in <strong>40</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C15" title="MSC2020">93C15</a> </td> <td class="space"> Control/observation systems governed by ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B70" title="MSC2020">93B70</a> </td> <td class="space"> Networked control </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afractional+order">fractional order</a>; <a href="/?q=ut%3Aquaternion-valued+neural+networks">quaternion-valued neural networks</a>; <a href="/?q=ut%3AMittag-Leffler+stability">Mittag-Leffler stability</a>; <a href="/?q=ut%3AMittag-Leffler+synchronization">Mittag-Leffler synchronization</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 1441.93209" data-ciurl="/ci/07201443" data-biburl="/bibtex/07201443.bib" data-amsurl="/amsrefs/07201443.bib" data-xmlurl="/xml/07201443.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07201443.pdf" title="Zbl 1441.93209 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.neunet.2018.04.015" aria-label="DOI for “Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons”" title="10.1016/j.neunet.2018.04.015">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, H.; Cao, J., Projective synchronization of fractional-order memristor-based neural networks, Neural Networks, 63, 1-9 (2015) · <a href="/1323.93036" class="nowrap">Zbl 1323.93036</a></td> </tr><tr> <td>[2]</td> <td class="space">Bao, H.; Park, J. 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