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We have created a new predator\u2013prey model by integrating the two species, Holling-III and Holling-I, which have a bifurcation within a specified parameter range. We discovered that this system possesses the stability of fixed points as well as several bifurcation behaviors. To accomplish this, the center manifold theorem and bifurcation theory are applied to create existence conditions for period-doubling bifurcations and Neimark\u2013Sacker bifurcations, which are depicted in the graph as distinct structures. Examples of numerical simulations include bifurcation diagrams, maximum Lyapunov exponents, and phase portraits, which demonstrate not just the validity of theoretical analysis but also complex dynamical behaviors and biological processes. Finally, the Ott\u2013Grebogi\u2013Yorke (OGY) method and phases of chaos control bifurcation were used to control the chaos of predator\u2013prey model in hibernating vertebrates.<\/jats:p>","DOI":"10.1142\/s0218127423501821","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T06:08:11Z","timestamp":1702361291000},"source":"Crossref","is-referenced-by-count":6,"title":["Dynamic Behaviors in a Discrete Model for Predator\u2013Prey Interactions Involving Hibernating Vertebrates"],"prefix":"10.1142","volume":"33","author":[{"given":"Mohammed O.","family":"Al-Kaff","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout, Yemen"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hamdy A.","family":"El-Metwally","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"El-Metwally M.","family":"Elabbasy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5010-601X","authenticated-orcid":false,"given":"Abd-Elalim A.","family":"Elsadany","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science and Humanities, Studies Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia"},{"name":"Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2023,12,11]]},"reference":[{"key":"S0218127423501821BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2007.08.029"},{"key":"S0218127423501821BIB002","volume-title":"National Geographic Complete Birds of North America","author":"Alderfer J. 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