{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:50:15Z","timestamp":1760057415594,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Research Fund Project of Yunnan Provincial Department of Education, China (Teacher Category)","award":["2025J1152"],"award-info":[{"award-number":["2025J1152"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this study, we research a nonautonomous, three-species, delayed reaction\u2013diffusion predator\u2013prey model (RDPPM). Firstly, we derive sufficient conditions to guarantee the existence of a strictly positive, spatially homogeneous periodic solution (SHPS) for the delayed, nonautonomous RDPPM. These conditions are obtained using the comparison theorem for delayed differential equations and the fixed point theorem. Secondly, we present sufficient conditions to ensure the global asymptotic stability of the SHPS for the delayed, nonautonomous RDPPM. These conditions are established through the application of the upper and lower solution method (UALSM) for delayed parabolic partial differential equations (PDEs), along with Lyapunov stability theory. Finally, to demonstrate the practical application of our results, we numerically validate the proposed conditions using a 2-periodic, delayed, nonautonomous RDPPM.<\/jats:p>","DOI":"10.3390\/axioms14020112","type":"journal-article","created":{"date-parts":[[2025,2,3]],"date-time":"2025-02-03T04:36:51Z","timestamp":1738557411000},"page":"112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Existence and Stability of a Periodic Solution of a Nonautonomous Delayed Reaction\u2013Diffusion Predator\u2013Prey Model"],"prefix":"10.3390","volume":"14","author":[{"given":"Lili","family":"Jia","sequence":"first","affiliation":[{"name":"Department of Basic Teaching, Dianchi College, Kunming 650228, China"},{"name":"School of Mathematical Sciences, V.C. & V.R. Key Lab of Sichuan Province, Sichuan Normal University, Chengdu 610066, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8797-0506","authenticated-orcid":false,"given":"Changyou","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1142\/S0218339006001933","article-title":"Permanence in a periodic predator-prey system with prey dispersal and predator density-independent","volume":"14","author":"Zhang","year":"2006","journal-title":"J. Biol. Syst."},{"key":"ref_2","first-page":"258","article-title":"Staged-structured Lotka-Volterra predator-prey models for pest management","volume":"203","author":"Shi","year":"2008","journal-title":"Appl. Math. 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