{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T02:18:34Z","timestamp":1767665914130},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2011,11]]},"abstract":"<jats:p> In this paper, some methodology in nonlinear dynamics is used to study a boundary-value problem of a nonlinear model arisen in phase transitions in a slender cylinder composed of a compressible hyperelastic material. We transform the original system of boundary-value problem to an initial-value (dynamical) problem of finding periodic solutions of coupled nonlinear autonomous oscillators in a four-dimensional space. Hopf-like bifurcation analysis of the periodic solutions of the system is studied. Both analytical and numerical solutions are obtained by using a nonlinear transformation formulation. The accuracy of analytical solutions is investigated by comparing with the numerical solutions. The engineering stress-strain curve is plotted and compared with that from the normal form equation, which is a simplification of the original system. <\/jats:p>","DOI":"10.1142\/s0218127411030489","type":"journal-article","created":{"date-parts":[[2012,1,2]],"date-time":"2012-01-02T20:28:03Z","timestamp":1325536083000},"page":"3231-3247","source":"Crossref","is-referenced-by-count":2,"title":["BIFURCATIONS IN A BOUNDARY-VALUE PROBLEM OF A NONLINEAR MODEL FOR STRESS-INDUCED PHASE TRANSITIONS"],"prefix":"10.1142","volume":"21","author":[{"given":"K. W.","family":"CHUNG","sequence":"first","affiliation":[{"name":"Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K. T.","family":"NG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.-H.","family":"DAI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,6]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1992.0013"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2005.1558"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7462(95)00043-7"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015620928121"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/s10659-005-9032-2"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2005.1557"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2007.0307"},{"key":"rf9","first-page":"229","volume":"44","author":"Dai H.-H.","journal-title":"Int. J. Non-Lin. Mech."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00126984"},{"key":"rf13","first-page":"1243","volume":"47","author":"Shaw J. A.","journal-title":"J. Mech. Phys. Solids"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S1359-6454(96)00189-9"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/S0749-6419(97)00062-4"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127411030489","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:24:40Z","timestamp":1565137480000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127411030489"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,11]]},"references-count":12,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2012,4,6]]},"published-print":{"date-parts":[[2011,11]]}},"alternative-id":["10.1142\/S0218127411030489"],"URL":"https:\/\/doi.org\/10.1142\/s0218127411030489","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,11]]}}}