{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T16:45:13Z","timestamp":1772037913859,"version":"3.50.1"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2002,8]]},"abstract":"<jats:p> The Melnikov theory for detecting subharmonic responses in periodically forced oscillators, the so-called subharmonic Melnikov theory, is a well-known technique within the dynamical system fields. The method succeeds in establishing the existence and stability of subharmonics in perturbed Hamiltonian systems as well as in discussing their bifurcations. But the parameter values estimated for the bifurcations are often found to be in poor agreement with those determined numerically. For damped and periodically driven oscillators, an approach which may substantially improve the agreement between analytical predictions and numerical investigations is proposed. The suggested technique consists in analyzing the forced regime of the oscillations by variational procedure, starting from the (approximate) solution for the free but damped oscillations. Applying this approach to the weakly nonlinear Duffing oscillator, it has been possible to detect analytically some subharmonics that the standard Melnikov theory fails to detect, thus demonstrating the ability of the proposed technique to capture much more of the dynamics. <\/jats:p>","DOI":"10.1142\/s0218127402005583","type":"journal-article","created":{"date-parts":[[2002,9,10]],"date-time":"2002-09-10T20:14:43Z","timestamp":1031688883000},"page":"1915-1923","source":"Crossref","is-referenced-by-count":6,"title":["THE SUBHARMONIC MELNIKOV THEORY FOR DAMPED AND DRIVEN OSCILLATORS REVISITED"],"prefix":"10.1142","volume":"12","author":[{"given":"SERGE BRUNO","family":"YAMGOU\u00c9","sequence":"first","affiliation":[{"name":"Laboratoire de M\u00e9canique, D\u00e9partement de Physique, Facult\u00e9 des Sciences, Universit\u00e9 de Yaound\u00e9 I, B.P. 812 Yaound\u00e9, Cameroun"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TIMOL\u00c9ON CR\u00c9PIN","family":"KOFAN\u00c9","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique, D\u00e9partement de Physique, Facult\u00e9 des Sciences, Universit\u00e9 de Yaound\u00e9 I, B.P. 812 Yaound\u00e9, Cameroun"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.33.4686"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.47.4585"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1088\/0031-8949\/54\/6\/001"},{"key":"rf4","unstructured":"B. D.\u00a0Greenspan and P. J.\u00a0Holmes, Nonlinear Dynamics and Turbulence, eds. G.\u00a0Barenblatt, G.\u00a0Iooss and D. D.\u00a0Joseph (Pitman, London, 1983)\u00a0pp. 172\u2013214."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01961239"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90082-X"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.41.726"},{"key":"rf8","first-page":"1","volume":"12","author":"Melnikov V. K.","journal-title":"Trans. Mosc. Math. Soc."},{"key":"rf9","volume-title":"Les m\u00e9thodes nouvelles de la m\u00e9caniques c\u00e9leste, Tome III","author":"Poincar\u00e9 H.","year":"1899"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749800173X"},{"key":"rf11","first-page":"262","volume":"18","author":"Wiggins S.","journal-title":"SIAM J. Appl. Math."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4067-7"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1137\/0523069"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1996.0080"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139995281317"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127402005583","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:06:51Z","timestamp":1565190411000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127402005583"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,8]]},"references-count":15,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2002,8]]}},"alternative-id":["10.1142\/S0218127402005583"],"URL":"https:\/\/doi.org\/10.1142\/s0218127402005583","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,8]]}}}