{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T21:38:25Z","timestamp":1761514705365,"version":"3.41.2"},"reference-count":28,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,1,16]],"date-time":"2021-01-16T00:00:00Z","timestamp":1610755200000},"content-version":"vor","delay-in-days":15,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971279","12001341"],"award-info":[{"award-number":["11971279","12001341"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>This paper investigates a stochastic two\u2010patch predator\u2010prey model with ratio\u2010dependent functional responses. First, the existence of a unique global positive solution is proved via the stochastic comparison theorem. Then, two different methods are used to discuss the long\u2010time properties of the solutions pathwise. Next, sufficient conditions for extinction and persistence in mean are obtained. Moreover, stochastic persistence of the model is discussed. Furthermore, sufficient conditions for the existence of an ergodic stationary distribution are derived by a suitable Lyapunov function. Next, we apply the main results in some special models. Finally, some numerical simulations are introduced to support the main results obtained. The results in this paper generalize and improve the previous related results.<\/jats:p>","DOI":"10.1155\/2021\/6671499","type":"journal-article","created":{"date-parts":[[2021,1,16]],"date-time":"2021-01-16T23:20:07Z","timestamp":1610839207000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Complex Dynamics of a Stochastic Two\u2010Patch Predator\u2010Prey Population Model with Ratio\u2010Dependent Functional 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