{"title":"On β-extinction and Stability of a Stochastic Lotka-Volterra System with Infinite Delay","authors":"Shu-fen Zhao","doi":"10.1007/s10255-024-1078-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, a stochastic Lotka-Volterra system with infinite delay is considered. A new concept of extinction, namely, the almost sure <i>β</i>-extinction is proposed and sufficient conditions for the solution to be almost sure <i>β</i>-extinction are obtained. When the positive equilibrium exists and the intensities of the noises are small enough, any solution of the system is attracted by the positive equilibrium. Finally, numerical simulations are carried out to support the results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1045 - 1059"},"PeriodicalIF":0.9000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-024-1078-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, a stochastic Lotka-Volterra system with infinite delay is considered. A new concept of extinction, namely, the almost sure β-extinction is proposed and sufficient conditions for the solution to be almost sure β-extinction are obtained. When the positive equilibrium exists and the intensities of the noises are small enough, any solution of the system is attracted by the positive equilibrium. Finally, numerical simulations are carried out to support the results.
期刊介绍:
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.