{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T08:07:16Z","timestamp":1773216436105,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T00:00:00Z","timestamp":1773100800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT\/Portugal","award":["UID\/04459\/2025"],"award-info":[{"award-number":["UID\/04459\/2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>In this paper I study a two-dimensional discrete-time evolutionary logistic-type model describing the coupled dynamics of population density and a continuously evolving trait. I provide a local bifurcation analysis of the equilibria, deriving explicit conditions for their existence and local stability. In particular, I show that the boundary and interior equilibria exchange stability through a transcritical bifurcation, and I characterize analytically the subsequent loss of stability of the interior equilibrium via period-doubling and Neimark\u2013Sacker bifurcations. Transversality is established in all cases, and the criticality of the bifurcations is determined through normal form and Lyapunov coefficient computations. I show that the period-doubling bifurcation can be supercritical or subcritical, while the Neimark\u2013Sacker bifurcation is generically nondegenerate and may be either supercritical or subcritical, depending on parameter values.<\/jats:p>","DOI":"10.3390\/math14060928","type":"journal-article","created":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T09:55:38Z","timestamp":1773136538000},"page":"928","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stability and Bifurcations in a Discrete-Time Eco-Evolutionary Logistic Model"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5991-9164","authenticated-orcid":false,"given":"Rafael","family":"Lu\u00eds","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade da Madeira, 9000-072 Funchal, Portugal"},{"name":"Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior T\u00e9cnico, University of Lisbon, 1649-004 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Elaydi, S.N., and Cushing, J.M. 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