{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T06:53:01Z","timestamp":1763535181577},"reference-count":22,"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":[[2012,8]]},"abstract":"<jats:p>Bifurcations of generic 2-2-1 heterodimensional cycles connecting to three saddles, in which two of them have two-dimensional unstable manifolds, are studied by setting up a local moving frame. Under a certain transversal condition, we firstly present the existence, uniqueness and noncoexistence of a 3-point heterodimensional cycle, 2-point heterodimensional or equidimensional cycle, 1-homoclinic cycle and 1-periodic orbit bifurcated from the 3-point heterodimensional cycle, and the bifurcation surfaces and bifurcation regions are located when the u-component [Formula: see text] of the vector [Formula: see text] under the Poincar\u00e9 mapping [Formula: see text] is nonzero. Conversely, we obtain some sufficient conditions such that the bifurcation of a 2-fold 1-periodic orbit occurs and a 1-periodic orbit coexists with the surviving heterodimensional cycle, showing some new bifurcation behaviors different from the well-known equidimensional cycles.<\/jats:p>","DOI":"10.1142\/s021812741250191x","type":"journal-article","created":{"date-parts":[[2012,9,17]],"date-time":"2012-09-17T08:52:34Z","timestamp":1347871954000},"page":"1250191","source":"Crossref","is-referenced-by-count":3,"title":["BIFURCATIONS OF 2-2-1 HETERODIMENSIONAL CYCLES UNDER TRANSVERSALITY CONDITION"],"prefix":"10.1142","volume":"22","author":[{"given":"DAN","family":"LIU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Xidian University, Xi'an, Shaanxi 710071, P. R. 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