{"title":"Dynamics of a multi-species lottery competition model in stochastic environments","authors":"Jiaqi Cheng, Xiaoying Han, Ming Liao","doi":"10.1142/s0219493722400287","DOIUrl":null,"url":null,"abstract":"<p>An <i>N</i>-dimensional lottery model for competition among <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>N</mi><mo>≥</mo><mn>2</mn></math></span><span></span> ecological species in stochastic environments is studied under the i.i.d. assumption. First, a system of nonlinear stochastic differential equations (SDEs) is developed as the diffusion approximation for the discrete lottery model. Then the existence and uniqueness of positive and bounded global solutions, as well as long-term dynamics for the solution are investigated. In particular, sufficient conditions under which extinction and persistence occur are constructed, respectively.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics and Dynamics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219493722400287","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
An N-dimensional lottery model for competition among ecological species in stochastic environments is studied under the i.i.d. assumption. First, a system of nonlinear stochastic differential equations (SDEs) is developed as the diffusion approximation for the discrete lottery model. Then the existence and uniqueness of positive and bounded global solutions, as well as long-term dynamics for the solution are investigated. In particular, sufficient conditions under which extinction and persistence occur are constructed, respectively.
期刊介绍：
This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view.
Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.
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