{"title":"圆柱体中一般 N 维扩散延迟洛特卡-伏特拉方程的稳定性和共存状态行波解","authors":"Yanling Tian, Shuyuan Shen, Jinji Yang","doi":"10.1093/imamci/dnae012","DOIUrl":null,"url":null,"abstract":"\n A general $N$-dimensional non-monotone delayed diffusive Lotka–Volterra model is considered in our paper. First, we obtain the global stability of the model subject to Neumann boundary condition by using a small delay result for delayed systems. Second, the limits at $+\\infty $ of bounded travelling wave solutions are confirmed by virtue of such global stability. Therefore, the existence of co-existence state travelling wave solutions is established. Finally, an example is given to illustrate the biological significance of the assumptions in the current paper.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability and co-existence state traveling wave solution for a general N-dimensional diffusive delayed Lotka-Volterra equation in a cylinder\",\"authors\":\"Yanling Tian, Shuyuan Shen, Jinji Yang\",\"doi\":\"10.1093/imamci/dnae012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n A general $N$-dimensional non-monotone delayed diffusive Lotka–Volterra model is considered in our paper. First, we obtain the global stability of the model subject to Neumann boundary condition by using a small delay result for delayed systems. Second, the limits at $+\\\\infty $ of bounded travelling wave solutions are confirmed by virtue of such global stability. Therefore, the existence of co-existence state travelling wave solutions is established. Finally, an example is given to illustrate the biological significance of the assumptions in the current paper.\",\"PeriodicalId\":56128,\"journal\":{\"name\":\"IMA Journal of Mathematical Control and Information\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IMA Journal of Mathematical Control and Information\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1093/imamci/dnae012\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Mathematical Control and Information","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1093/imamci/dnae012","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Stability and co-existence state traveling wave solution for a general N-dimensional diffusive delayed Lotka-Volterra equation in a cylinder
A general $N$-dimensional non-monotone delayed diffusive Lotka–Volterra model is considered in our paper. First, we obtain the global stability of the model subject to Neumann boundary condition by using a small delay result for delayed systems. Second, the limits at $+\infty $ of bounded travelling wave solutions are confirmed by virtue of such global stability. Therefore, the existence of co-existence state travelling wave solutions is established. Finally, an example is given to illustrate the biological significance of the assumptions in the current paper.
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