{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:59:39Z","timestamp":1760144379145,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,9]],"date-time":"2024-04-09T00:00:00Z","timestamp":1712620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we present a survey about the latest results in global stability concerning the discrete-time evolutionary Ricker competition model with n species, in both, autonomous and periodic models. The main purpose is to convey some arguments and new ideas concerning the techniques for showing global asymptotic stability of fixed points or periodic cycles in these kind of discrete-time models. In order to achieve this, some open problems and conjectures related to the evolutionary Ricker competition model are presented, which may be a starting point to study global stability, not only in other competition models, but in predator\u2013prey models and Leslie\u2013Gower-type models as well.<\/jats:p>","DOI":"10.3390\/axioms13040246","type":"journal-article","created":{"date-parts":[[2024,4,9]],"date-time":"2024-04-09T08:55:12Z","timestamp":1712652912000},"page":"246","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Open Problems and Conjectures in the Evolutionary Periodic Ricker Competition Model"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5991-9164","authenticated-orcid":false,"given":"Rafael","family":"Lu\u00eds","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Madeira, Campus Universit\u00e1rio da Penteada, 9020-105 Funchal, Portugal"},{"name":"Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Tecnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,9]]},"reference":[{"key":"ref_1","unstructured":"Darwin, C. (1859). The Origin of Species, Avenel Books."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1111\/nrm.12074","article-title":"On the dynamics of ecolutionary competition models","volume":"28","author":"Ackleh","year":"2015","journal-title":"Nat. Resurce Model."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"AlSharawi, Z., and Cushing, J. (2014). 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