{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T19:04:38Z","timestamp":1784142278745,"version":"3.55.0"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,3]]},"abstract":"<jats:p> It has previously been established that in a prestressed incompressible elastic plate, a near-critical instability mode can interact resonantly with two non-critical vibration modes and that the evolution equations for the three modes take the form d<jats:sup>2<\/jats:sup> A<jats:sub>1<\/jats:sub>\/d\u03c4<jats:sup>2<\/jats:sup> = -c<jats:sub>0<\/jats:sub>A<jats:sub>1<\/jats:sub> - c<jats:sub>1<\/jats:sub>|A<jats:sub>1<\/jats:sub>|<jats:sup>2<\/jats:sup>A<jats:sub>1<\/jats:sub> - \u03b3<jats:sub>1<\/jats:sub>\u0100<jats:sub>2<\/jats:sub>\u0100<jats:sub>3<\/jats:sub>, dA<jats:sub>2<\/jats:sub>\/d\u03c4 = \u03b3<jats:sub>2<\/jats:sub>\u0100<jats:sub>1<\/jats:sub>\u0100<jats:sub>3<\/jats:sub> and dA<jats:sub>3<\/jats:sub>\/d\u03c4 = \u03b3<jats:sub>3<\/jats:sub>\u0100<jats:sub>1<\/jats:sub>\u0100<jats:sub>2<\/jats:sub>, where a bar denotes complex conjugation, \u03c4 is a slow time variable and c<jats:sub>0<\/jats:sub>, c<jats:sub>1<\/jats:sub>, \u03b3<jats:sub>1<\/jats:sub>, \u03b3<jats:sub>2<\/jats:sub>, \u03b3<jats:sub>3<\/jats:sub> are real constants. In this paper, we analyze these amplitude equations using dynamical systems theory. Regions of the parametric space that correspond to bounded solutions are determined and some explicit representations of the bounded solutions are obtained. It is shown that the resonant-triad interaction can lead to chaotic motions. <\/jats:p>","DOI":"10.1142\/s0218127409023378","type":"journal-article","created":{"date-parts":[[2009,5,28]],"date-time":"2009-05-28T06:49:43Z","timestamp":1243493383000},"page":"903-921","source":"Crossref","is-referenced-by-count":2,"title":["CHAOTIC MOTION AND HAMILTONIAN DYNAMICS OF A PRESTRESSED INCOMPRESSIBLE ELASTIC PLATE DUE TO RESONANT-TRIAD INTERACTIONS"],"prefix":"10.1142","volume":"19","author":[{"given":"JIBIN","family":"LI","sequence":"first","affiliation":[{"name":"Center for Nonlinear Science Studies, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. 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