{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T10:55:56Z","timestamp":1648896956095},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p> This paper is Part II of an earlier paper dealing with the numerical study of a two-dimensional nonautonomous ordinary differential equation with a strong cubic nonlinearity, and an external periodical excitation of period \u03c4 = 2\u03c0\/\u03c9 (amplitude E). In the absence of this excitation, this equation of Duffing type does not give rise to self-oscillations. Part I was essentially devoted to analyze the harmonics behavior of period \u03c4 solutions, more precisely the behavior of rank-p harmonics according to the points of the parameter plane (\u03c9,E). The present Part II deals with period k\u03c4 solutions related to a cascade of closed fold bifurcation curves related to fractional harmonics p\/k, k = 3, p = 3,4,\u2026. With respect to the organization of bifurcation curves associated with rank-p harmonics of the basic period \u03c4, this study shows that the situation is a lot more complex for the sequence of bifurcation curves related to rank-p\/3 harmonics. <\/jats:p>","DOI":"10.1142\/s0218127409023597","type":"journal-article","created":{"date-parts":[[2009,8,17]],"date-time":"2009-08-17T09:02:26Z","timestamp":1250499746000},"page":"1227-1254","source":"Crossref","is-referenced-by-count":0,"title":["BEHAVIOR OF HARMONICS GENERATED BY A DUFFING TYPE EQUATION WITH A NONLINEAR DAMPING: PART II"],"prefix":"10.1142","volume":"19","author":[{"given":"H\u00c9DI","family":"KHAMMARI","sequence":"first","affiliation":[{"name":"Institut Sup\u00e9rieur des Sciences Appliqu\u00e9es et de, Technologie de Kairouan, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CHRISTIAN","family":"MIRA","sequence":"additional","affiliation":[{"name":"GESNLA,19 rue d'Occitanie, 31130 Quint, France"},{"name":"Istituto di Scienze Economiche, University of Urbino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127491000117"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"rf3","volume-title":"Nonlinear Oscillations in Physical Systems","author":"Hayashi C.","year":"1964"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1109\/TCS.1984.1085495","volume":"31","author":"Kawakami H.","journal-title":"IEEE Trans. Circuits Syst."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405014076"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/0413"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127491000464"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127491000269"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497001527"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1980.tb29708.x"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409023597","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:02:18Z","timestamp":1565136138000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409023597"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":10,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,4]]}},"alternative-id":["10.1142\/S0218127409023597"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409023597","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}