{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:36:19Z","timestamp":1772292979457,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:p> This paper is concerned with the asymptotic behavior of the solutions u(x,t) of the Swift\u2013Hohenberg equation with quintic nonlinearity on a one-dimensional domain (0, L). With \u03b1 and the length L of the domain regarded as bifurcation parameters, branches of nontrivial solutions bifurcating from the trivial solution at certain points are shown. Local behavior of these branches are also studied. Global bounds for the solutions u(x,t) are established and then the global attractor is investigated. Finally, with the help of a center manifold analysis, two types of structures in the bifurcation diagrams are presented when the bifurcation points are closer, and their stabilities are analyzed. <\/jats:p>","DOI":"10.1142\/s0218127409024542","type":"journal-article","created":{"date-parts":[[2009,12,15]],"date-time":"2009-12-15T11:45:55Z","timestamp":1260877555000},"page":"2927-2937","source":"Crossref","is-referenced-by-count":12,"title":["BIFURCATION ANALYSIS OF THE SWIFT\u2013HOHENBERG EQUATION WITH QUINTIC NONLINEARITY"],"prefix":"10.1142","volume":"19","author":[{"given":"QINGKUN","family":"XIAO","sequence":"first","affiliation":[{"name":"Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P. R. China"}]},{"given":"HONGJUN","family":"GAO","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2005.06.009"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1137\/06067794X"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1137\/040604479"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1137\/060670262"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1137\/070707622"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00253709"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-073X(03)00021-9"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2004.01.043"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1137\/050647232"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(98)00038-4"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.15.319"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1137\/070709128"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409024542","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:10:11Z","timestamp":1565125811000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409024542"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":12,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2009,9]]}},"alternative-id":["10.1142\/S0218127409024542"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409024542","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}