{"title":"Long time behavior of a Lotka–Volterra competition system with two dynamical resources and density-dependent motility","authors":"Jianping Gao, Wenyan Lian","doi":"10.1016/j.matcom.2024.11.008","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we consider a Lotka–Volterra competition system with two dynamical resources and density-dependent motility under the homogeneous Neumann boundary condition. Here, we put the two competing species into a predator–prey system, and assume that the two competing species as predators can feed on different preys and that the preys as resources admit temporal dynamics including spatial movement, intrinsic birth–death kinetics and loss due to predation. When the distributions of prey’s resources can be homogeneous, by using some proper Lyapunov functionals and applying LaSalle’s invariant principle, we obtain that the solution can converge to the positive steady state exponentially or to the competitive exclusion steady states algebraically as time goes to infinity. Our finding shows that the consideration of temporal dynamics on the resources can lead to the coexistence of two competitors in some parameter conditions regardless of their dispersal rates. When the distributions of prey’s resources are spatially heterogeneous, we conduct several numerical simulations in different combinations of dispersal strategy and the distributions of prey’s resources, and we show that the non-random dispersal and heterogeneous distributions of prey’s resources can affect the fates of two competitors.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"230 ","pages":"Pages 131-148"},"PeriodicalIF":4.4000,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Computers in Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037847542400449X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider a Lotka–Volterra competition system with two dynamical resources and density-dependent motility under the homogeneous Neumann boundary condition. Here, we put the two competing species into a predator–prey system, and assume that the two competing species as predators can feed on different preys and that the preys as resources admit temporal dynamics including spatial movement, intrinsic birth–death kinetics and loss due to predation. When the distributions of prey’s resources can be homogeneous, by using some proper Lyapunov functionals and applying LaSalle’s invariant principle, we obtain that the solution can converge to the positive steady state exponentially or to the competitive exclusion steady states algebraically as time goes to infinity. Our finding shows that the consideration of temporal dynamics on the resources can lead to the coexistence of two competitors in some parameter conditions regardless of their dispersal rates. When the distributions of prey’s resources are spatially heterogeneous, we conduct several numerical simulations in different combinations of dispersal strategy and the distributions of prey’s resources, and we show that the non-random dispersal and heterogeneous distributions of prey’s resources can affect the fates of two competitors.
期刊介绍:
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
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They also include considerations about computer hardware for simulation and about special software and compilers.
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