{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:18Z","timestamp":1740103698758,"version":"3.37.3"},"reference-count":38,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T00:00:00Z","timestamp":1586822400000},"content-version":"unspecified","delay-in-days":0,"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":["11371230","ZR2019MA003"],"award-info":[{"award-number":["11371230","ZR2019MA003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["11371230","ZR2019MA003"],"award-info":[{"award-number":["11371230","ZR2019MA003"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,4,14]]},"abstract":"<jats:p>This paper puts forward a class of ratio-dependent Leslie predator-prey models. Firstly, a neutral delay predator-prey model with ratio dependence and impulse control is established and the existence of positive periodic solutions is proved by the coincidence degree theory. Secondly, a stochastic disturbance Leslie model of Smith growth is obtained when the interference of white noise is taken into consideration and the impact of delay is ignored. Applying It<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mover accent=\"true\"><mml:mtext>o<\/mml:mtext><mml:mo>^<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>\u2019s formula, we get the conditions of system persistence and extinction. Finally we verify the correctness of theoretical analysis with numerical simulations.<\/jats:p>","DOI":"10.1155\/2020\/8428269","type":"journal-article","created":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T23:32:26Z","timestamp":1586907146000},"page":"1-15","source":"Crossref","is-referenced-by-count":4,"title":["Periodic Solution of a Neutral Delay Leslie Predator-Prey Model and the Effect of Random Perturbation on the Smith Growth Model"],"prefix":"10.1155","volume":"2020","author":[{"given":"Tongtong","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4689-695X","authenticated-orcid":true,"given":"Wencai","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, 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