{"title":"具有马尔可夫切换的一维随机Gilpin-Ayala系统的随机持久性和消光性","authors":"Lei Liu, Xiaoyan Yu","doi":"10.1109/ICICIP.2014.7010307","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the permanence, extinction for one-dimensional stochastic Gilpin-Ayala system with Markovian switching. By using Lyapunov method and some novel techniques, some sufficient conditions are obtained which ensure the permanence, extinction for the system. In the case of η = 1, sufficient and necessary conditions for permanence and extinction are obtained. Two numerical examples are provided to illustrate the effectiveness and the benefits of the proposed result.","PeriodicalId":408041,"journal":{"name":"Fifth International Conference on Intelligent Control and Information Processing","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stochastic permanence and extinction for one-dimensional stochastic Gilpin-Ayala systems with Markovian switching\",\"authors\":\"Lei Liu, Xiaoyan Yu\",\"doi\":\"10.1109/ICICIP.2014.7010307\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider the permanence, extinction for one-dimensional stochastic Gilpin-Ayala system with Markovian switching. By using Lyapunov method and some novel techniques, some sufficient conditions are obtained which ensure the permanence, extinction for the system. In the case of η = 1, sufficient and necessary conditions for permanence and extinction are obtained. Two numerical examples are provided to illustrate the effectiveness and the benefits of the proposed result.\",\"PeriodicalId\":408041,\"journal\":{\"name\":\"Fifth International Conference on Intelligent Control and Information Processing\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fifth International Conference on Intelligent Control and Information Processing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICICIP.2014.7010307\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fifth International Conference on Intelligent Control and Information Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICICIP.2014.7010307","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stochastic permanence and extinction for one-dimensional stochastic Gilpin-Ayala systems with Markovian switching
In this paper, we consider the permanence, extinction for one-dimensional stochastic Gilpin-Ayala system with Markovian switching. By using Lyapunov method and some novel techniques, some sufficient conditions are obtained which ensure the permanence, extinction for the system. In the case of η = 1, sufficient and necessary conditions for permanence and extinction are obtained. Two numerical examples are provided to illustrate the effectiveness and the benefits of the proposed result.
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