{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T18:57:28Z","timestamp":1777316248664,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T00:00:00Z","timestamp":1757030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Tarim University President Fund","award":["TDZKQN201823"],"award-info":[{"award-number":["TDZKQN201823"]}]},{"name":"Tarim University President Fund","award":["TDZKSS201904"],"award-info":[{"award-number":["TDZKSS201904"]}]},{"name":"Tarim University President Fund","award":["415105003"],"award-info":[{"award-number":["415105003"]}]},{"name":"central government supports the discipline construction projects of local universities","award":["TDZKQN201823"],"award-info":[{"award-number":["TDZKQN201823"]}]},{"name":"central government supports the discipline construction projects of local universities","award":["TDZKSS201904"],"award-info":[{"award-number":["TDZKSS201904"]}]},{"name":"central government supports the discipline construction projects of local universities","award":["415105003"],"award-info":[{"award-number":["415105003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study examines a discrete-time predator\u2013prey model constructed via piecewise constant discretization of its continuous counterpart. Through comprehensive qualitative and dynamical analyses, we reveal a rich set of nonlinear phenomena, encompassing Neimark\u2013Sacker bifurcation, flip bifurcation, and codimension-two bifurcations corresponding to 1:2, 1:3, and 1:4 resonances. Rigorous analysis of these bifurcation scenarios, conducted via center manifold theory and bifurcation methods, establishes a robust mathematical framework for their characterization. Numerical simulations corroborate the theoretical predictions, exposing intricate dynamical phenomena such as quasiperiodic oscillations and chaotic attractors. Our results demonstrate that resonance-driven bifurcations are potent drivers of ecological complexity in discrete systems, acting as key determinants that orchestrate the emergent dynamics of populations\u2014a finding with profound implications for interpreting patterns in real-world ecosystems subject to discrete generations or seasonal pulses.<\/jats:p>","DOI":"10.3390\/sym17091459","type":"journal-article","created":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T07:46:17Z","timestamp":1757058377000},"page":"1459","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multiple Bifurcation Analysis in a Discrete-Time Predator\u2013Prey Model with Holling IV Response Function"],"prefix":"10.3390","volume":"17","author":[{"given":"Yun","family":"Liu","sequence":"first","affiliation":[{"name":"College of Information Engineering, Tarim University, Alar 843300, China"},{"name":"Key Laboratory of Tarim Oasis Agricaluture, Tarim University, Ministry of Education, Alar 843300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lifeng","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Tarim University, Alar 843300, China"},{"name":"Key Laboratory of Tarim Oasis Agricaluture, Tarim University, Ministry of Education, Alar 843300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0988-1505","authenticated-orcid":false,"given":"Xijuan","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Tarim University, Alar 843300, China"},{"name":"Key Laboratory of Tarim Oasis Agricaluture, Tarim University, Ministry of Education, Alar 843300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.jde.2024.07.016","article-title":"Coexistence of heterogeneous predator-prey systems with prey-dependent dispersal","volume":"409","author":"Tang","year":"2024","journal-title":"J. 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