{"title":"具有狩猎延迟的三阶段结构捕食者-猎物模型的Hopf分岔","authors":"Shun-yi Li, Wenwu Liu","doi":"10.1109/ICSAI.2012.6223231","DOIUrl":null,"url":null,"abstract":"A three stage-structured prey-predator model with hunting delay is studied. The characteristic equations of the boundary and positive equilibrium are analyzed and the conditions of the positive equilibrium occurring Hopf bifurcation are given by applying the theorem of Hopf bifurcation. By using Nyquist criterion, the estimation of the length of delay to preserve stability is obtained. Finally, numerical simulation and brief conclusion are given.","PeriodicalId":164945,"journal":{"name":"2012 International Conference on Systems and Informatics (ICSAI2012)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Hopf bifurcation in a three stage-structured prey-predator model with hunting delay\",\"authors\":\"Shun-yi Li, Wenwu Liu\",\"doi\":\"10.1109/ICSAI.2012.6223231\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A three stage-structured prey-predator model with hunting delay is studied. The characteristic equations of the boundary and positive equilibrium are analyzed and the conditions of the positive equilibrium occurring Hopf bifurcation are given by applying the theorem of Hopf bifurcation. By using Nyquist criterion, the estimation of the length of delay to preserve stability is obtained. Finally, numerical simulation and brief conclusion are given.\",\"PeriodicalId\":164945,\"journal\":{\"name\":\"2012 International Conference on Systems and Informatics (ICSAI2012)\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-05-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 International Conference on Systems and Informatics (ICSAI2012)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICSAI.2012.6223231\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 International Conference on Systems and Informatics (ICSAI2012)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICSAI.2012.6223231","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hopf bifurcation in a three stage-structured prey-predator model with hunting delay
A three stage-structured prey-predator model with hunting delay is studied. The characteristic equations of the boundary and positive equilibrium are analyzed and the conditions of the positive equilibrium occurring Hopf bifurcation are given by applying the theorem of Hopf bifurcation. By using Nyquist criterion, the estimation of the length of delay to preserve stability is obtained. Finally, numerical simulation and brief conclusion are given.
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