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A detailed mathematical analysis explores the local stability of equilibria and the emergence of flip and Neimark\u2013Sacker bifurcations, leading to periodic and quasi-periodic dynamics. Special cases with vanishing Allee constants reveal critical impacts on species persistence and extinction. Numerical simulations support the analytical results and illustrate diverse regimes, from stability to complex fractal trajectories. Furthermore, a chaos control strategy based on bifurcation analysis is proposed to stabilize the system dynamics near desired states. The findings highlight the intricate interplay between predation and dual Allee effects in shaping long-term ecological outcomes. In addition, our analysis is supported by several foundational works on nonlinear dynamics, bifurcation theory, and discrete-time predator\u2013prey modeling, which provide important theoretical tools for understanding complex ecological systems [ Gakkhar &amp; Singh ,\u00a0 2012 ;\u00a0 Jing &amp; Yang ,\u00a0 2006 ;\u00a0 Kuznetsov ,\u00a0 1997 ;\u00a0 Liu &amp; Xiao ,\u00a0 2007 ;\u00a0 MacDonald ,\u00a0 2008 ;\u00a0 Wan ,\u00a0 1978 ;\u00a0 Wiggins ,\u00a0 2003 ;\u00a0 Rocha &amp; Taha ,\u00a0 2023 ;\u00a0 Singh et al. ,\u00a0 2019 ;\u00a0 Hassan &amp; Goldar ,\u00a0 2023 ;\u00a0 Goldar ,\u00a0 2025 ;\u00a0 Goldar et al. ,\u00a0 2025b ].<\/jats:p>","DOI":"10.1142\/s0218127426500380","type":"journal-article","created":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T09:29:09Z","timestamp":1765790949000},"source":"Crossref","is-referenced-by-count":0,"title":["Dynamics and Bifurcation Analysis of a Discrete Predator\u2013Prey Model with Dual Allee Effects"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4601-3419","authenticated-orcid":false,"given":"Sk Sarif","family":"Hassan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Pingla Thana Mahavidyalaya, Maligram, West Midnapore, West Bengal 721140, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6956-4379","authenticated-orcid":false,"given":"Sujay","family":"Goldar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Pingla Thana Mahavidyalaya, Maligram, West Midnapore, West Bengal 721140, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3812-8918","authenticated-orcid":false,"given":"Ahmed Ali","family":"Mohsen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Open Education College, Baghdad, Iraq"},{"name":"Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5592-3182","authenticated-orcid":false,"given":"Rasmikanta","family":"Pati","sequence":"additional","affiliation":[{"name":"SUIIT, Sambalpur University, Jyoti Vihar, Burla, Sambalpur, Odisha 768004, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,12,13]]},"reference":[{"key":"S0218127426500380BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.09.077"},{"key":"S0218127426500380BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/3033"},{"key":"S0218127426500380BIB003","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004918920121"},{"key":"S0218127426500380BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s40435-017-0347-1"},{"key":"S0218127426500380BIB005","volume-title":"Insect Predator\u2013Prey Dynamics: Ladybird Beetles and Biological Control","author":"Dixon A. 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