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Global Stability of a Lotka-Volterra Competition-Diffusion-Advection System with Different Positive Diffusion Distributions

Lili Chen, Shilei Lin, Yanfeng Zhao
2021 Axioms  
In this paper, the problem of a LotkaVolterra competitiondiffusionadvection system between two competing biological organisms in a spatially heterogeneous environments is investigated.  ...  When two biological organisms are competing for different fundamental resources, and their advection and diffusion strategies follow different positive diffusion distributions, the functions of specific  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/axioms10030166 fatcat:loqdbvhrvvf3pluss6ombm5o4i

Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity

Benlong Xu, Hongyan Jiang
2017 Journal of Nonlinear Science and its Applications  
This paper mainly studies the dynamics of a Lotka-Volterra reaction-diffusion-advection model for two competing species which disperse by both random diffusion and advection along environmental gradient  ...  This is a remarkable different result with that obtained by He and Ni recently for corresponding systems without advection [X. He, W.-M.  ...  Concluding remarks We study the dynamics of the Lotka-Volterra reaction-diffusion-advection model (1.3), in which the two competing species have equal total resources but different resource distribution  ... 
doi:10.22436/jnsa.010.11.46 fatcat:q6qasvctgreylezgvba55rbq2m

Page 3804 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
Zhidong (PRC-XINJ; Urumgi); Chen, Lansun (PRC-ASBJ; Beijing) Uniform persistence and existence of strictly positive solutions in nonautonomous Lotka-Volterra competitive systems with delays.  ...  The focus of this paper is to present new criteria for global sta- bility and uniform persistence in certain n-species competition Lotka-Volterra models with discrete and continuous delays.  ... 

Global Directed Dynamic Behaviors of a Lotka-Volterra Competition-Diffusion-Advection System

Lili Chen, Shilei Lin, Yanfeng Zhao
2021 Axioms  
This paper investigates the problem of the global directed dynamic behaviors of a Lotka-Volterra competition-diffusion-advection system between two organisms in heterogeneous environments.  ...  The two organisms not only compete for different basic resources, but also the advection and diffusion strategies follow the dispersal towards a positive distribution.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/axioms10030195 fatcat:brbvxuiktfemhdn5k7rdx6oyfe

Global existence and uniform boundedness in advective Lotka-Volterra competition system with nonlinear diffusion [article]

Qi Wang, Jingyue Yang, Feng Yu
2016 arXiv   pre-print
This paper investigates reaction-advection-diffusion systems with Lotka-Volterra dynamics subject to homogeneous Neumann boundary conditions.  ...  Our results suggest that attraction (positive taxis) inhibits blowups in Lotka-Volterra competition systems.  ...  In the absence of advection with χ = 0, and when D 1 (u) ≡ D 1 , α = 1, (1.1) reduces to the classical diffusive Lotka-Volterra competition model        u t = D 1 ∆u + (a 1 − b 1 u − c 1 v)u, x  ... 
arXiv:1605.05308v1 fatcat:d5wykxwgxfeivnaxpw6od7hul4

Fortune favours the brave: Movement responses shape demographic dynamics in strongly competing populations

Jonathan R. Potts, Sergei V. Petrovskii
2017 Journal of Theoretical Biology  
Mathematically, these movement responses are encoded in an advection 98 term, leading to a system of reaction-advection-diffusion equations. These naturally combine 99  ...  the first model dating back to Lotka (1932) and 45 Volterra (1926), so popularly termed the Lotka-Volterra competition (LVC) model.  ...  Generation of interfaces for lotka-volterra competition-588 diffusion system with large interaction rates. J. Differ. Equations, 235, 586-608. Switch in fate due to movement strategies.  ... 
doi:10.1016/j.jtbi.2017.03.011 pmid:28322873 fatcat:fdfjj64qfjeydljucpv4rno7sq

Directed Movement of Predators and the Emergence of Density-Dependence in Predator–Prey Models

R. Arditi, Yu. Tyutyunov, A. Morgulis, V. Govorukhin, I. Senina
2001 Theoretical Population Biology  
, completely different from the Lotka Volterra rule assumed at the local scale. ]  ...  Locally, the populations follow the simple Lotka Volterra interaction. We also assume predator reproduction and mortality to be negligible in comparison with the time scale of migration.  ...  This is a contribution of the French CoReV research grouping. Part of this research was done while Yu.  ... 
doi:10.1006/tpbi.2001.1513 pmid:11444960 fatcat:m5uwh62r3raydowgbven7jjfci

Invasion and coexistence of competition-diffusion-advection system with heterogeneous vs homogeneous resources

Benlong Xu, Hongyan Jiang
2018 Discrete and continuous dynamical systems. Series B  
The ratio of advection strength and diffusion rate of the species with heterogeneous distribution plays a crucial role in the dynamics behavior of the system.  ...  This paper mainly study the dynamics of a Lotka-Volterra reactiondiffusion-advection model for two competing species which disperse by both random diffusion and advection along environmental gradient.  ...  We study the dynamics of the Lotka-Volterra reactiondiffusion-advection model, in which the two competing species have equal total resources but different strategy of resource distribution.  ... 
doi:10.3934/dcdsb.2018136 fatcat:ku6wivjbu5dlzkyniyksm2hdp4

Global dynamics of a general Lotka-Volterra competition-diffusion system in heterogeneous environments

Qian Guo, ,School of Mathematical Sciences, East China Normal University, Shanghai 200241, China, Xiaoqing He, Wei-Ming Ni, ,School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China, ,Chinese University of Hong Kong – Shenzhen, Shenzhen, China, ,School of Mathematics, University of Minnesota, MN 55455, USA
2020 Discrete and Continuous Dynamical Systems. Series A  
This indicates the importance and subtleties of the roles of heterogeneous competition coefficients in the dynamics of the Lotka-Volterra competition-diffusion systems.  ...  We establish the main result that determines the global dynamics of the system under a general criterion.  ...  The research of X. He is supported in part by NSFC(11601155) and Science and Technology Commission of Shanghai Municipality (No. 18dz2271000); the research of W.-M.  ... 
doi:10.3934/dcds.2020290 fatcat:nvolnfia3vcprigleinwh2x6yy

Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

King-Yeung Lam, Shuang Liu, Yuan Lou
2020 Mathematics in Applied Sciences and Engineering  
We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction–diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially  ...  Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplanktongrowth, and spatial spread of epidemic disease.  ...  for two-species Lotka-Volterra competition models.  ... 
doi:10.5206/mase/10644 fatcat:62yycbm6z5cv7egfz5mzhe6wq4

Evolution of Dispersal with Starvation Measure and Coexistence

Yong-Jung Kim, Ohsang Kwon
2016 Bulletin of Mathematical Biology  
The evolutional selection and coexistence of such starvation measures are studied within the context of Lotka-Volterra type competition model of two species.  ...  In this paper we compare three different ways of measuring starvation by applying them to starvation driven diffusion.  ...  ≡ 0, 0 ≤ v(x, 0) ≡ 0, x ∈ Ω, (10) which is a Lotka-Volterra type competition model of two species.  ... 
doi:10.1007/s11538-016-0142-8 pmid:26817757 fatcat:xruopdawazgrbjibjvf4fdcfra

Spatial segregation limit of traveling wave solutions for a fully nonlinear strongly coupled competitive system [article]

Léo Girardin
2021 arXiv   pre-print
The paper is concerned with a singular limit for the bistable traveling wave problem in a very large class of two-species fully nonlinear parabolic systems with competitive reaction terms.  ...  Assuming existence of traveling waves and enough compactness, we derive and characterize the limiting problem. The assumptions and results are discussed in detail.  ...  Global well-posedness of advective lotkavolterra compe- tition systems with nonlinear diffusion.  ... 
arXiv:2010.12205v4 fatcat:jbbla7nk5ba3loyfgt3phtulx4

Evolution of dispersal in advective homogeneous environments

Li Ma, ,College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, Jiangxi, China, De Tang, ,School of Mathematics(Zhuhai), Sun Yat-sen University, Zhuhai 519082, Guangdong, China
2020 Discrete and Continuous Dynamical Systems. Series A  
Zhou, On a Lotka-Volterra competition system: diffusion vs advection, Calc. Var.  ...  This paper is devoted to studying a two-species competition model in a one-dimensional advective homogeneous environment, where the two species are identical except their diffusion rates and advection  ...  As long as advection terms incorporated in classical Lotka-Volterra competition-diffusion systems, the study of the persistence for the corresponding single equation seems nontrivial, and the global dynamics  ... 
doi:10.3934/dcds.2020247 fatcat:jwqfdzolhzfwtcmxif4wy4d7si

Selected topics on reaction-diffusion-advection models from spatial ecology [article]

King-Yeung Lam, Shuang Liu, Yuan Lou
2020 arXiv   pre-print
We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially  ...  Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplankton growth, and spatial spread of epidemic disease. Open problems and conjectures are presented.  ...  KYL and YL are partially supported by the NSF grant DMS-1853561; SL was partially supported by the Outstanding Innovative Talents Cultivation Funded Programs 2018 of Renmin Univertity of China and the  ... 
arXiv:2004.07978v2 fatcat:75hojs7re5ey3n67ih5pqwgbzy

An explicit solution of Burgers equation with stationary point source

Jaywan Chung, Yong-Jung Kim, Marshall Slemrod
2014 Journal of Differential Equations  
Lotka-Volterra competition systems for two species are tested, where one species follows the starvation driven diffusion and the other follows the linear diffusion.  ...  Various issues such as the global asymptotic stability, convergence to an ideal free distribution, the extinction and coexistence are discussed.  ...  Then the competition system (16) (17) (18) has two critical solutions, where (θ l,m , 0) is globally asymptotically stable among positive solutions.  ... 
doi:10.1016/j.jde.2014.05.046 fatcat:jb4ki3inp5e4hoqxjrmntsne3i
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