{"title":"具有跳跃的随机捕食者种群密度依赖的捕食者-食饵模型的灭绝和持续","authors":"O. Borysenko, O. Borysenko","doi":"10.17721/1812-5409.2023/1.4","DOIUrl":null,"url":null,"abstract":"The non-autonomous stochastic density dependent predator-prey model with Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises is investigated. Corresponding system of stochastic differential equations has a unique, positive, global (no explosions in a finite time) solution. Sufficient conditions are obtained for extinction, non-persistence in the mean, weak and strong persistence in the mean of a predator and prey population densities in the considered stochastic predator-prey model.","PeriodicalId":33822,"journal":{"name":"Visnik Kiivs''kij nacional''nij universitet imeni Tarasa Sevcenka Istoria","volume":"56 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extinction and persistence in stochastic predator population density-dependent predator-prey model with jumps\",\"authors\":\"O. Borysenko, O. Borysenko\",\"doi\":\"10.17721/1812-5409.2023/1.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The non-autonomous stochastic density dependent predator-prey model with Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises is investigated. Corresponding system of stochastic differential equations has a unique, positive, global (no explosions in a finite time) solution. Sufficient conditions are obtained for extinction, non-persistence in the mean, weak and strong persistence in the mean of a predator and prey population densities in the considered stochastic predator-prey model.\",\"PeriodicalId\":33822,\"journal\":{\"name\":\"Visnik Kiivs''kij nacional''nij universitet imeni Tarasa Sevcenka Istoria\",\"volume\":\"56 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Visnik Kiivs''kij nacional''nij universitet imeni Tarasa Sevcenka Istoria\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17721/1812-5409.2023/1.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Visnik Kiivs''kij nacional''nij universitet imeni Tarasa Sevcenka Istoria","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17721/1812-5409.2023/1.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Extinction and persistence in stochastic predator population density-dependent predator-prey model with jumps
The non-autonomous stochastic density dependent predator-prey model with Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises is investigated. Corresponding system of stochastic differential equations has a unique, positive, global (no explosions in a finite time) solution. Sufficient conditions are obtained for extinction, non-persistence in the mean, weak and strong persistence in the mean of a predator and prey population densities in the considered stochastic predator-prey model.