Document Zbl 1349.37036

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These impulsive excitations do not necessarily act on the equilibria of the non-smooth system, which leads to a barrier for the conventional nonlinear techniques. How to solve this barrier is an issue on the top of our agenda. Normally, these non-smooth factors were considered term by term. Using Hamiltonian function and principle perturbation theory, a reasonable compromise is applied to detect the extended Melnikov function based on the characteristics of the non-smooth homoclinic orbits with multiple jump discontinuities. It is a critical step that the perturbation solutions are examined from two points of view in order to obtain their small-perturbation expansions. Furthermore, the Melnikov function is employed to obtain the criteria for chaotic motion, which shows the effects of these impulsive excitations, the perturbation of damping and external forcing on the behaviors of the non-smooth dynamical system. The efficiency of the criteria for chaotic motion obtained in this paper is verified by bifurcation diagram, phase portraits and Poincaré surface of section.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6658913">Cited in <strong>17</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A37D45" title="MSC2020">37D45</a> </td> <td class="space"> Strange attractors, chaotic dynamics of systems with hyperbolic behavior </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37C29" title="MSC2020">37C29</a> </td> <td class="space"> Homoclinic and heteroclinic orbits for dynamical systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A37" title="MSC2020">34A37</a> </td> <td class="space"> Ordinary differential equations with impulses </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34C37" title="MSC2020">34C37</a> </td> <td class="space"> Homoclinic and heteroclinic solutions to ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34C28" title="MSC2020">34C28</a> </td> <td class="space"> Complex behavior and chaotic systems of ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aimpulsive+differential+system">impulsive differential system</a>; <a href="/?q=ut%3Anon-smooth+homoclinic+orbit">non-smooth homoclinic orbit</a>; <a href="/?q=ut%3Achaos">chaos</a>; <a href="/?q=ut%3AMelnikov+method">Melnikov method</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 1349.37036" data-ciurl="/ci/06658913" data-biburl="/bibtex/06658913.bib" data-amsurl="/amsrefs/06658913.bib" data-xmlurl="/xml/06658913.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06658913.pdf" title="Zbl 1349.37036 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/s11071-016-2800-7" aria-label="DOI for “Chaotic threshold for non-smooth system with multiple impulse effect”" title="10.1007/s11071-016-2800-7">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">Wang, W., Zhang, Q.C., Feng, J.J.: Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation. 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