{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:32:20Z","timestamp":1763389940761,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009392","name":"Prince Sattam Bin Abdulaziz University","doi-asserted-by":"publisher","award":["PSAU\/2024\/01\/29834"],"award-info":[{"award-number":["PSAU\/2024\/01\/29834"]}],"id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The Basener and Ross mathematical model is widely recognized for its ability to characterize the interaction between the population dynamics and resource utilization of Easter Island. In this study, we develop and investigate a discrete-time version of the Basener and Ross model. First, the existence and the stability of fixed points for the present model are investigated. Next, we investigated various bifurcation scenarios by establishing criteria for the occurrence of different types of codimension-one bifurcations, including flip and Neimark\u2013Sacker bifurcations. These criteria are derived using the center manifold theorem and bifurcation theory. Furthermore, we demonstrated the existence of codimension-two bifurcations characterized by 1:2, 1:3, and 1:4 resonances, emphasizing the model\u2019s complex dynamical structure. Numerical simulations are employed to validate and illustrate the theoretical predictions. Finally, through bifurcation diagrams, maximal Lyapunov exponents, and phase portraits, we uncover a diversity of dynamical characteristics, including limit cycles, periodic solutions, and chaotic attractors.<\/jats:p>","DOI":"10.3390\/computation13010011","type":"journal-article","created":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T03:38:41Z","timestamp":1736221121000},"page":"11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bifurcation Analysis of a Discrete Basener\u2013Ross Population Model: Exploring Multiple Scenarios"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5010-601X","authenticated-orcid":false,"given":"A. A.","family":"Elsadany","sequence":"first","affiliation":[{"name":"Mathematics Department, College of Science and Humanities Studies in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4256-968X","authenticated-orcid":false,"given":"A. M.","family":"Yousef","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt"}]},{"given":"S. A.","family":"Ghazwani","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science and Humanities Studies in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}]},{"given":"A. S.","family":"Zaki","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Aswan University, Aswan 81528, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Liu, Y., and Li, X. (2021). Dynamics of a discrete predator-prey model with Holling-II functional response. Int. J. Biomath., 14.","DOI":"10.1142\/S1793524521500686"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3589","DOI":"10.1002\/mma.8005","article-title":"Stability and bifurcation analysis of discrete predator-prey model with nonlinear prey harvesting and prey refuge","volume":"45","author":"Shu","year":"2022","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2567","DOI":"10.1080\/00036811.2022.2030724","article-title":"Complicate bifurcation behaviors of a discrete predator-prey model with group defense and nonlinear harvesting in prey","volume":"102","author":"Yao","year":"2023","journal-title":"Appl. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.chaos.2016.09.020","article-title":"Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response","volume":"93","author":"Salman","year":"2016","journal-title":"Chaos Solitons Fractals"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.cam.2019.01.012","article-title":"Stability and further analytical bifurcation behaviors of Moran-Ricker model with delayed density dependent birth rate regulation","volume":"355","author":"Yousef","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1850116","DOI":"10.1142\/S021812741850116X","article-title":"Stability and bifurcation analysis of a delayed discrete predator-prey model","volume":"28","author":"Yousef","year":"2018","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2050237","DOI":"10.1142\/S0218127420502375","article-title":"Stability, analytic bifurcation structure and chaos control in a mutual interference host-parasitoid model","volume":"30","author":"Yousef","year":"2020","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1080\/09692290.2020.1830829","article-title":"Climate change and international political economy: Between collapse and transformation","volume":"28","author":"Paterson","year":"2020","journal-title":"Rev. Int. Political Econ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1877","DOI":"10.1137\/22M1494336","article-title":"Sustainability or societal collapse: Dynamics and bifurcations of the handy model","volume":"22","author":"Tonnelier","year":"2023","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"357","DOI":"10.3390\/world3020020","article-title":"Environmental determinism vs. social dynamics: Prehistorical and historical examples","volume":"3","author":"Sargentis","year":"2022","journal-title":"World"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1736","DOI":"10.1137\/19M1279526","article-title":"Population collapse in elite-dominated societies: A differential equations model without differential equations","volume":"19","author":"Akhavan","year":"2020","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7675","DOI":"10.1016\/j.ifacol.2017.08.1139","article-title":"Structural effects and aggregation in a social-network model of natural resource consumption","volume":"50","author":"Manzoor","year":"2017","journal-title":"IFAC-PapersOnLine"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ecolecon.2018.10.018","article-title":"Learning from the ancient maya: Exploring the impact of drought on population dynamics","volume":"157","author":"Kuil","year":"2019","journal-title":"Ecol. Econ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"105094","DOI":"10.1016\/j.jas.2020.105094","article-title":"A model-based approach to the tempo of \u201ccollapse\u201d: The case of rapa nui (easter island)","volume":"116","author":"DiNapoli","year":"2020","journal-title":"J. Archaeol. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.tpb.2021.03.002","article-title":"Model of neo-malthusian population anticipating future changes in resources","volume":"140","author":"Michel","year":"2021","journal-title":"Theor. Popul. Biol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1016\/j.ecolecon.2017.11.007","article-title":"The dynamics of human\u2013environment interactions in the collapse of the classic maya","volume":"146","author":"Roman","year":"2018","journal-title":"Ecol. Econ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107861","DOI":"10.1016\/j.ecolecon.2023.107861","article-title":"Environmental change and ecosystem functioning drive transitions in social-ecological systems: A stylized modelling approach","volume":"211","author":"Eppinga","year":"2023","journal-title":"Ecol. Econ."},{"key":"ref_18","first-page":"119","article-title":"The simple economics of easter island: A ricardo-malthus model of renewable resource use","volume":"88","author":"Brander","year":"1998","journal-title":"Am. Econ. Rev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1137\/S0036139903426952","article-title":"Booming and crashing populations and easter island","volume":"65","author":"Basener","year":"2004","journal-title":"SIAM J. Appl. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/0169-5347(86)90018-2","article-title":"Chaos in ecological systems: The coals that newcastle forgot","volume":"1","author":"Schaffer","year":"1986","journal-title":"Trends Ecol. Evol."},{"key":"ref_21","first-page":"29","article-title":"Dynamics of a discrete population model for extinction and sustainability in ancient civilizations","volume":"12","author":"Basener","year":"2008","journal-title":"Nonlinear Dyn. Psychol. Life Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s40435-020-00637-8","article-title":"Generalized flip and strong resonances bifurcations of a predator-prey model","volume":"9","author":"Eskandari","year":"2021","journal-title":"Int. J. Dyn. Control"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"112923","DOI":"10.1016\/j.chaos.2022.112923","article-title":"Stability, co-dimension two bifurcations and chaos control of a host-parasitoid model with mutual interference","volume":"166","author":"Yousef","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Salman, S.M., and Elsadany, A.A. (2023). Analytical bifurcation and strong resonances of a discrete bazykin-berezovskaya predator-prey model with Allee effect. Int. J. Biomath., 16.","DOI":"10.1142\/S1793524522501364"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"115171","DOI":"10.1016\/j.cam.2023.115171","article-title":"Codimension one and codimension two bifurcations in a discrete Kolmogorov type predator-prey model","volume":"428","author":"Yousef","year":"2023","journal-title":"J. Comput. Appl. Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.chaos.2005.10.081","article-title":"Complex dynamic behaviors of a discrete-time predator-prey system","volume":"32","author":"Liu","year":"2007","journal-title":"Chaos Solitons Fractals"},{"key":"ref_27","unstructured":"Guckenheimer, J., and Holmes, P. (2013). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer Science & Business Media."},{"key":"ref_28","unstructured":"Kuznetsov, Y.A. (1998). Elements of Applied Bifurcation Theory, Springer."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Kuznetsov, I., Kuznetsov, Y.A., and Meijer, H.G. (2019). Numerical Bifurcation Analysis of Maps, Cambridge University Press.","DOI":"10.1017\/9781108585804"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Strogatz, S.H. (2018). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, CRC Press.","DOI":"10.1201\/9780429399640"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/1\/11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:23:59Z","timestamp":1759919039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/1\/11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,7]]},"references-count":30,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["computation13010011"],"URL":"https:\/\/doi.org\/10.3390\/computation13010011","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2025,1,7]]}}}