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We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to…

Analysis of PDEs · Mathematics 2007-07-13 E. C. M. Crooks , E. N. Dancer , D. Hilhorst

This paper is concerned with the existence of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. Considering highly competitive systems, a simple "high frequency or…

Analysis of PDEs · Mathematics 2016-12-08 Léo Girardin

In this paper, we consider two species chemotaxis systems with Lotka-Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system…

Analysis of PDEs · Mathematics 2020-10-23 T. B. Issa , R. B Salako , W. Shen

Our interest here is to find the invader in a two species, diffusive and competitive Lotka-Volterra system in the particular case of travelling wave solutions. We investigate the role of diffusion in homogeneous domains. We might expect a…

Analysis of PDEs · Mathematics 2015-07-01 Léo Girardin , Grégoire Nadin

This paper is concerned with the limit, as the interspecific competition rate goes to infinity, of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. We distinguish…

Analysis of PDEs · Mathematics 2017-12-15 Léo Girardin , Grégoire Nadin

This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…

Analysis of PDEs · Mathematics 2017-03-08 Emmanuel Risler

We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under…

Analysis of PDEs · Mathematics 2017-10-17 Yihong Du , Chang-Hong Wu

The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and…

Classical Analysis and ODEs · Mathematics 2022-01-19 Shanshan Chen , Junping Shi , Zhisheng Shuai , Yixiang Wu

In this paper, we mainly consider the speed selection problem for the classical Lotka-Volterra competition system. For the first time, we propose a sufficient and necessary condition for this long-standing problem from a new point of view.…

Analysis of PDEs · Mathematics 2025-04-23 Chang-Hong Wu , Dongyuan Xiao , Maolin Zhou

This paper is concerned with the existence of traveling wave solutions for diffusive two-species Lotka-Volterra systems with delay in both the reaction and diffusion terms without monotonicity. We extend the partial or cross monotone…

Analysis of PDEs · Mathematics 2023-03-21 William Barker

This paper is concerned with a nonlocal diffusion Lotka-Volterra type competition model that consisting of a native species and an invasive species in a one-dimensional habitat with free boundaries. We prove the well-posedness of the system…

Dynamical Systems · Mathematics 2019-05-24 Jia-Feng Cao , Wan-Tong Li , Jie Wang

Reaction-diffusion systems with a Lotka-Volterra-type reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among $m$ ecological species for a limited resource necessary to…

Populations and Evolution · Quantitative Biology 2018-11-01 Lorenzo Contento , Danielle Hilhorst , Masayasu Mimura

This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…

Analysis of PDEs · Mathematics 2026-03-25 Yang-Yang Yan , Wei-Jie Sheng

In this paper we prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation and to a model of…

Dynamical Systems · Mathematics 2012-05-21 José Valero

The global asymptotic behavior of the classical diffusive Lotka-Volterra competition model with stage structure is studied. A complete classification of the global dynamics is given for the weak competition case. It is shown that under…

Dynamical Systems · Mathematics 2019-09-10 Shanshan Chen , Junping Shi

Defeat and success of the competitive invasion of a populated area is described with a standard Lotka-Volterra competition model. The resident is adapted to the heterogeneous living conditions, i.e., its motion is modelled as…

Populations and Evolution · Quantitative Biology 2017-10-12 Michael Bengfort , Ivo Siekmann , Horst Malchow

In this paper, we study three two competing species Lotka-Volterra competition models on finite connected graphs, with Dirichlet, Neumann or no boundary conditions. We get that when time goes to infinity, either one specie extincts while…

Analysis of PDEs · Mathematics 2022-10-26 Yuanyang Hu , Chengxia Lei

Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation…

Probability · Mathematics 2021-05-10 N. N. Nguyen , G. Yin

This paper investigates the global well-posedness of a class of reaction-advection-diffusion models with nonlinear diffusion and Lotka-Volterra dynamics. We prove the existence and uniform boundedness of the global-in-time solutions to the…

Analysis of PDEs · Mathematics 2019-05-21 Qi Wang , Jingyue Yang , Feng Yu

We present properties of Lotka-Volterra equations describing ecological competition among a large number of competing species. First we extend to the case of a non-homogeneous niche space stability conditions for solutions representing…

Populations and Evolution · Quantitative Biology 2009-07-22 Emilio Hernandez-Garcia , Cristobal Lopez , Simone Pigolotti , Ken H. Andersen