{"title":"两物种竞争模型中离散时滞产生的振荡与共存","authors":"Xiaolan Wang, Chanaka Kottegoda, Chunhua Shan, Qihua Huang","doi":"10.3934/dcdsb.2023156","DOIUrl":null,"url":null,"abstract":"One of the shortcomings of the classical Lotka-Volterra competition model is that both species' births are assumed to be instantaneous, whereas developmental and maturation processes may cause time delays. We extend the Lotka-Volterra competition model to a delayed model based on a single species delayed model in this paper. The effects of two discrete delays on competition outcomes are investigated. Our theoretical and numerical results show that delays can cause the loss of stability of equilibria and the emergence of periodic solutions (i.e., population density oscillations) via Hopf bifurcation, lead to exclusion by changing the stability of coexistence equilibrium, and boost coexistence even if the coexistence equilibrium point does not exist.","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Oscillations and coexistence generated by discrete delays in a two-species competition model\",\"authors\":\"Xiaolan Wang, Chanaka Kottegoda, Chunhua Shan, Qihua Huang\",\"doi\":\"10.3934/dcdsb.2023156\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"One of the shortcomings of the classical Lotka-Volterra competition model is that both species' births are assumed to be instantaneous, whereas developmental and maturation processes may cause time delays. We extend the Lotka-Volterra competition model to a delayed model based on a single species delayed model in this paper. The effects of two discrete delays on competition outcomes are investigated. Our theoretical and numerical results show that delays can cause the loss of stability of equilibria and the emergence of periodic solutions (i.e., population density oscillations) via Hopf bifurcation, lead to exclusion by changing the stability of coexistence equilibrium, and boost coexistence even if the coexistence equilibrium point does not exist.\",\"PeriodicalId\":51015,\"journal\":{\"name\":\"Discrete and Continuous Dynamical Systems-Series B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete and Continuous Dynamical Systems-Series B\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/dcdsb.2023156\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete and Continuous Dynamical Systems-Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcdsb.2023156","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Oscillations and coexistence generated by discrete delays in a two-species competition model
One of the shortcomings of the classical Lotka-Volterra competition model is that both species' births are assumed to be instantaneous, whereas developmental and maturation processes may cause time delays. We extend the Lotka-Volterra competition model to a delayed model based on a single species delayed model in this paper. The effects of two discrete delays on competition outcomes are investigated. Our theoretical and numerical results show that delays can cause the loss of stability of equilibria and the emergence of periodic solutions (i.e., population density oscillations) via Hopf bifurcation, lead to exclusion by changing the stability of coexistence equilibrium, and boost coexistence even if the coexistence equilibrium point does not exist.
期刊介绍:
Centered around dynamics, DCDS-B is an interdisciplinary journal focusing on the interactions between mathematical modeling, analysis and scientific computations. The mission of the Journal is to bridge mathematics and sciences by publishing research papers that augment the fundamental ways we interpret, model and predict scientific phenomena. The Journal covers a broad range of areas including chemical, engineering, physical and life sciences. A more detailed indication is given by the subject interests of the members of the Editorial Board.