{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:41:49Z","timestamp":1761489709634},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,6,30]]},"abstract":"<jats:p> The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui &amp; Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie\u2013Gower functional response as well as that of Beddington\u2013DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values. <\/jats:p>","DOI":"10.1142\/s0218127415400143","type":"journal-article","created":{"date-parts":[[2015,7,16]],"date-time":"2015-07-16T07:23:03Z","timestamp":1437031383000},"page":"1540014","source":"Crossref","is-referenced-by-count":9,"title":["Bifurcation and Stability in a Delayed Predator\u2013Prey Model with Mixed Functional Responses"],"prefix":"10.1142","volume":"25","author":[{"given":"R.","family":"Yafia","sequence":"first","affiliation":[{"name":"Ibn Zohr University, Polydisciplinary Faculty of Ouarzazate, B.P. 638, Ouarzazate, Morocco"}]},{"given":"M. A.","family":"Aziz-Alaoui","sequence":"additional","affiliation":[{"name":"Normandie University, France"},{"name":"ULH, LMAH, F-76600 Le Havre, FR CNRS 3335, ISCN, 25 rue Philippe Lebon, 76600 Le Havre, France"}]},{"given":"H.","family":"Merdan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, TOBB University of Economics and Technology, S\u00f6g\u00fct\u00f6z\u00fc Cad. No. 43 06530, S\u00f6g\u00fct\u00f6z\u00fc, Ankara, Turkey"}]},{"given":"J. J.","family":"Tewa","sequence":"additional","affiliation":[{"name":"UMI 209 UMMISCO, GRIMCAPE, Yaounde, Cameroon"}]}],"member":"219","published-online":{"date-parts":[[2015,7,16]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(03)90096-6"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(97)00491-4"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(82)90243-8"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-93073-7"},{"key":"rf5","first-page":"180","volume":"122","author":"Faria T.","year":"1995","journal-title":"J. Diff. Eqs."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7920-9"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9892-2"},{"key":"rf8","volume-title":"Delay Differential Equations, with Applications in Population Dynamics","author":"Kuang Y.","year":"1993"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-93107-9"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2005.10.003"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(00)00141-7"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2004.11.001"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00111-4"},{"key":"rf14","first-page":"1","volume":"84","author":"Yu S.","year":"2014","journal-title":"Adv. Diff. Eqs."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127415400143","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:03:50Z","timestamp":1565118230000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127415400143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,30]]},"references-count":14,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2015,7,16]]},"published-print":{"date-parts":[[2015,6,30]]}},"alternative-id":["10.1142\/S0218127415400143"],"URL":"https:\/\/doi.org\/10.1142\/s0218127415400143","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,30]]}}}