{"title":"具有Holling I型功能响应和时滞的捕食模型的数学分析","authors":"N. Sharmila, C. Gunasundari","doi":"10.28919/cmbn/8014","DOIUrl":null,"url":null,"abstract":". We examine two prey and one predator models with Holling type I functional behaviours in this paper. To demonstrate the system’s permanence and boundedness, we used a discrete-time delay. Through the use of traditional mathematical techniques, the effects of random variations in the environment and time delay on the model’s stability are analytically examined. The stability and Hopf-Bifurcation for the competition model are also described and shown. A few numerical computations are provided to demonstrate the efficacy of the theoretical findings.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Mathematical analysis of prey predator models with Holling type I functional responses and time delay\",\"authors\":\"N. Sharmila, C. Gunasundari\",\"doi\":\"10.28919/cmbn/8014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We examine two prey and one predator models with Holling type I functional behaviours in this paper. To demonstrate the system’s permanence and boundedness, we used a discrete-time delay. Through the use of traditional mathematical techniques, the effects of random variations in the environment and time delay on the model’s stability are analytically examined. The stability and Hopf-Bifurcation for the competition model are also described and shown. A few numerical computations are provided to demonstrate the efficacy of the theoretical findings.\",\"PeriodicalId\":44079,\"journal\":{\"name\":\"Communications in Mathematical Biology and Neuroscience\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Biology and Neuroscience\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.28919/cmbn/8014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Biology and Neuroscience","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.28919/cmbn/8014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
Mathematical analysis of prey predator models with Holling type I functional responses and time delay
. We examine two prey and one predator models with Holling type I functional behaviours in this paper. To demonstrate the system’s permanence and boundedness, we used a discrete-time delay. Through the use of traditional mathematical techniques, the effects of random variations in the environment and time delay on the model’s stability are analytically examined. The stability and Hopf-Bifurcation for the competition model are also described and shown. A few numerical computations are provided to demonstrate the efficacy of the theoretical findings.
期刊介绍:
Communications in Mathematical Biology and Neuroscience (CMBN) is a peer-reviewed open access international journal, which is aimed to provide a publication forum for important research in all aspects of mathematical biology and neuroscience. This journal will accept high quality articles containing original research results and survey articles of exceptional merit.