{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T09:06:47Z","timestamp":1745312807445,"version":"3.37.3"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2018,6,15]]},"abstract":"<jats:p> This article investigates the oscillatory patterns of the following discrete-time Rosenzweig\u2013MacArthur model [Formula: see text] The system describes the evolution and interaction of the populations of two associated species (prey and predator) from generation to generation. We show that this system can exhibit co-dimension-1 bifurcations (flip and Neimark\u2013Sacker bifurcations) as [Formula: see text] crosses some critical values and codimension-2 bifurcations (1:2, 1:3, and 1:4 resonances) for certain critical values of [Formula: see text] at the positive equilibrium point. The normal form theory and the center manifold theorem are used to obtain the normal forms. For codimension-2 bifurcations, the bifurcation diagrams are established by using these normal forms along the orbits of differential equations. Numerical simulations are presented to confirm the theoretical results. <\/jats:p>","DOI":"10.1142\/s021812741850075x","type":"journal-article","created":{"date-parts":[[2018,6,21]],"date-time":"2018-06-21T03:03:03Z","timestamp":1529550183000},"page":"1850075","source":"Crossref","is-referenced-by-count":7,"title":["Analysis of Oscillatory Patterns of a Discrete-Time Rosenzweig\u2013MacArthur Model"],"prefix":"10.1142","volume":"28","author":[{"given":"Xiaoqin P.","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Computer and Information Sciences, Mississippi Valley State University, Itta Bena, MS 38941, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6567-6138","authenticated-orcid":false,"given":"Liancheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kennesaw State University, Marietta, GA 30060, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,6,21]]},"reference":[{"volume-title":"Normal Forms and Bifurcation of Planar Vector Fields","year":"2004","author":"Chow S. N.","key":"S021812741850075XBIB001"},{"key":"S021812741850075XBIB002","first-page":"1","volume":"48","author":"Du Y.","year":"2006","journal-title":"Fields Instit. Commun."},{"key":"S021812741850075XBIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3978-7"},{"key":"S021812741850075XBIB004","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2006.6.559"},{"key":"S021812741850075XBIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.081"},{"key":"S021812741850075XBIB006","doi-asserted-by":"crossref","DOI":"10.1007\/b98869","volume-title":"Mathematical Biology","author":"Murray J. D.","year":"2003"},{"key":"S021812741850075XBIB007","doi-asserted-by":"publisher","DOI":"10.1086\/282272"},{"volume-title":"Complex Population Dynamics","year":"2003","author":"Turchin P.","key":"S021812741850075XBIB008"},{"key":"S021812741850075XBIB009","doi-asserted-by":"publisher","DOI":"10.1137\/080728512"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812741850075X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:38:21Z","timestamp":1565109501000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812741850075X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,15]]},"references-count":9,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2018,6,21]]},"published-print":{"date-parts":[[2018,6,15]]}},"alternative-id":["10.1142\/S021812741850075X"],"URL":"https:\/\/doi.org\/10.1142\/s021812741850075x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2018,6,15]]}}}