{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:42:40Z","timestamp":1740120160989,"version":"3.37.3"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11771197"],"award-info":[{"award-number":["11771197"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the High-Level Talent Project of Colleges and Universities in Guang- dong Province","award":["QBS201501"],"award-info":[{"award-number":["QBS201501"]}]},{"name":"the Guangdong Natural Science Foundation of China","award":["2017A030313030"],"award-info":[{"award-number":["2017A030313030"]}]},{"name":"the Startup Foundation for Doctors of Lingnan Normal University","award":["ZL1605"],"award-info":[{"award-number":["ZL1605"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2018,6,30]]},"abstract":"<jats:p> In this paper, we consider a one-dimensional difference equation with three parameters, the derivative of which at a fixed point has an eigenvalue [Formula: see text] as the parameters are all zero. In the case that both nondegeneracy conditions of the flip bifurcation and the generalized flip bifurcation are not satisfied, by computing normal form, we give the nondegeneracy condition and transversality condition of the codimension-3 flip bifurcation. Moreover, by discussing the number of positive zeros of a cubic function in a neighborhood of the origin, we show the bifurcation scenario and give the parameter conditions, respectively, that the normal form of the equation possesses three 2-cycles, two 2-cycles, only one 2-cycle or none. <\/jats:p>","DOI":"10.1142\/s0218127418500906","type":"journal-article","created":{"date-parts":[[2018,7,17]],"date-time":"2018-07-17T04:26:51Z","timestamp":1531801611000},"page":"1850090","source":"Crossref","is-referenced-by-count":1,"title":["Codimension-3 Flip Bifurcation of a Class of Difference Equations"],"prefix":"10.1142","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0116-865X","authenticated-orcid":false,"given":"Jiyu","family":"Zhong","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingwang","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mathematics, Sichuan University, Chengdu 610064, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,7,17]]},"reference":[{"key":"S0218127418500906BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-11832-0"},{"key":"S0218127418500906BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s10255-013-0207-5"},{"key":"S0218127418500906BIB003","volume-title":"An Introduction to Difference Equations","author":"Elaydi S.","year":"2005","edition":"3"},{"key":"S0218127418500906BIB004","volume-title":"Elements of Applied Bifurcation Theory","author":"Kuznetsov Y.","year":"1998","edition":"2"},{"key":"S0218127418500906BIB005","doi-asserted-by":"publisher","DOI":"10.1080\/10236190701483145"},{"key":"S0218127418500906BIB006","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2010.14.159"},{"key":"S0218127418500906BIB007","first-page":"559","volume":"3","author":"Liu X.","year":"2006","journal-title":"Discr. Contin. Dyn. Syst. Ser. 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