{"title":"捕食者中具有Holling II递增函数的随机捕食者-猎物模型。","authors":"Youlin Huang, Wanying Shi, Chunjin Wei, Shuwen Zhang","doi":"10.1080/17513758.2020.1859146","DOIUrl":null,"url":null,"abstract":"<p><p>This paper is concerned with a stochastic predator-prey model with Holling II increasing function in the predator. By applying the Lyapunov analysis method, we demonstrate the existence and uniqueness of the global positive solution. Then we show there is a stationary distribution which implies the stochastic persistence of the predator and prey in the model. Moreover, we obtain respectively sufficient conditions for weak persistence in the mean and extinction of the prey and extinction of the predator. Finally, some numerical simulations are given to illustrate our main results and the discussion and conclusion are presented.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"15 1","pages":"1-18"},"PeriodicalIF":1.8000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1859146","citationCount":"15","resultStr":"{\"title\":\"A stochastic predator-prey model with Holling II increasing function in the predator.\",\"authors\":\"Youlin Huang, Wanying Shi, Chunjin Wei, Shuwen Zhang\",\"doi\":\"10.1080/17513758.2020.1859146\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>This paper is concerned with a stochastic predator-prey model with Holling II increasing function in the predator. By applying the Lyapunov analysis method, we demonstrate the existence and uniqueness of the global positive solution. Then we show there is a stationary distribution which implies the stochastic persistence of the predator and prey in the model. Moreover, we obtain respectively sufficient conditions for weak persistence in the mean and extinction of the prey and extinction of the predator. Finally, some numerical simulations are given to illustrate our main results and the discussion and conclusion are presented.</p>\",\"PeriodicalId\":48809,\"journal\":{\"name\":\"Journal of Biological Dynamics\",\"volume\":\"15 1\",\"pages\":\"1-18\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/17513758.2020.1859146\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Biological Dynamics\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1080/17513758.2020.1859146\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ECOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Biological Dynamics","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1080/17513758.2020.1859146","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECOLOGY","Score":null,"Total":0}
A stochastic predator-prey model with Holling II increasing function in the predator.
This paper is concerned with a stochastic predator-prey model with Holling II increasing function in the predator. By applying the Lyapunov analysis method, we demonstrate the existence and uniqueness of the global positive solution. Then we show there is a stationary distribution which implies the stochastic persistence of the predator and prey in the model. Moreover, we obtain respectively sufficient conditions for weak persistence in the mean and extinction of the prey and extinction of the predator. Finally, some numerical simulations are given to illustrate our main results and the discussion and conclusion are presented.
期刊介绍：
Journal of Biological Dynamics, an open access journal, publishes state of the art papers dealing with the analysis of dynamic models that arise from biological processes. The Journal focuses on dynamic phenomena at scales ranging from the level of individual organisms to that of populations, communities, and ecosystems in the fields of ecology and evolutionary biology, population dynamics, epidemiology, immunology, neuroscience, environmental science, and animal behavior. Papers in other areas are acceptable at the editors’ discretion. In addition to papers that analyze original mathematical models and develop new theories and analytic methods, the Journal welcomes papers that connect mathematical modeling and analysis to experimental and observational data. The Journal also publishes short notes, expository and review articles, book reviews and a section on open problems.
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