{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:35:20Z","timestamp":1760146520099,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T00:00:00Z","timestamp":1731456000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds for the Central Universities","award":["2572022BC04"],"award-info":[{"award-number":["2572022BC04"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper investigates the stability of predator\u2013prey models within multi-patch environments, with a particular focus on the influence of cross-dispersion across patches. We apply Kirchhoff\u2019s matrix tree theorem and Liapunov\u2019s method to derive criteria related to the cross-dispersion topology, thus solving the challenge of determining global asymptotic stability conditions. The method incorporates realistic ecological interactions and spatial heterogeneity, offering a framework for stability analysis. Our findings demonstrate that an appropriate level of cross-dispersion can effectively mitigate oscillations and foster convergence toward equilibrium. Two numerical examples validate these theoretical results and demonstrate the feasibility and effectiveness of the model across multiple patches.<\/jats:p>","DOI":"10.3390\/axioms13110783","type":"journal-article","created":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T09:59:11Z","timestamp":1731491951000},"page":"783","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Stability of a Predator\u2013Prey Model with Cross-Dispersal in a Multi-Patch Environment"],"prefix":"10.3390","volume":"13","author":[{"given":"Keyao","family":"Xu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China"}]},{"given":"Keyu","family":"Peng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China"}]},{"given":"Shang","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1038\/23876","article-title":"Metapopulation dynamics","volume":"396","author":"Hanski","year":"1998","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1038\/35065725","article-title":"Exploring complex networks","volume":"410","author":"Strogatz","year":"2001","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1038\/326388a0","article-title":"Habitat fragmentation and the stability of predator-prey interactions","volume":"326","author":"Kareiva","year":"1987","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3411","DOI":"10.3934\/dcds.2020031","article-title":"Asymptotic population abundance of a two-patch system with asymmetric diffusion","volume":"40","author":"Fang","year":"2020","journal-title":"Discret. 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