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In this work, we investigate the long-time dynamics of a two species competition model of Lotka-Volterra type with nonlocal diffusions. One of the species, with density $v(t,x)$, is assumed to be a native in the environment (represented by…

Analysis of PDEs · Mathematics 2024-03-29 Yihong Du , Wenjie Ni , Linfei Shi

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

The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or unbounded boundary. Such a model with a free boundary describes the spreading…

Dynamical Systems · Mathematics 2020-02-11 Lianzhang Bao , Wenxian Shen

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 investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…

Analysis of PDEs · Mathematics 2025-11-21 Qian Qin , JinJing Jiao , Zhiguo Wang , Hua Nie

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

We investigate the long term behavior for a class of competition-diffusion systems of Lotka-Volterra type for two competing species in the case of low regularity assumptions on the data. Due to the coupling that we consider the system…

Analysis of PDEs · Mathematics 2008-06-06 Marco Squassina

In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time…

Dynamical Systems · Mathematics 2021-05-13 Lingyu Liu

The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these…

Analysis of PDEs · Mathematics 2024-10-01 Maicon Sonego , Enrique Zuazua

We consider the classical two-species Lotka-Volterra competition-diffusion system in the strong-weak competition case. When the corresponding minimal speed of the traveling waves is not linear determined, we establish the precise asymptotic…

Analysis of PDEs · Mathematics 2022-01-13 Chang-Hong Wu , Dongyuan Xiao , Maolin Zhou

This article is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic ecological model. The local existence and uniqueness of a classical…

Analysis of PDEs · Mathematics 2014-05-20 Mei Li

The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or an unbounded boundary. Such a model with a free boundary describes the…

Dynamical Systems · Mathematics 2019-03-01 Lianzhang Bao , Wenxian Shen

In this paper, we consider a Leslie-Gower predator-prey model in one-dimensional environment. We study the asymptotic behavior of two species evolving in a domain with a free boundary. Sufficient conditions for spreading success and…

Analysis of PDEs · Mathematics 2018-12-03 Yunfeng Liu , Zhiming Guo , Mohammad El Smaily , Lin Wang

A horizontal $N$-dimensional plane, having a diffusion of its own, exchanges with the lower half space. There, a reaction-diffusion process, modelled by a free boundary problem, takes place. We wish to understand whether, and how, the free…

Analysis of PDEs · Mathematics 2022-12-21 Luis A. Caffarelli , Jean-Michel Roquejoffre , Ignacio Tomasetti

In this paper, we study a diffusive Lotka-Volterra competition model under homogeneous Dirichlet boundary conditions. We shall discuss the effects of dispersal rate and spatial heterogeneity on population dynamics. More precisely, we…

Analysis of PDEs · Mathematics 2021-03-04 Qi Wang

In this work, we show how to obtain a free boundary problem as the limit of a fully non linear elliptic system of equations that models population segregation (Gause-Lotka-Volterra type). We study the regularity of the solutions. In…

Analysis of PDEs · Mathematics 2015-06-11 Veronica Quitalo

We investigate the global dynamics of a special case of the classical Lotka-Volterra competition-diffusion system in spatially heterogeneous environment. This model indicates that the evolution of the density of the predator is independent…

Dynamical Systems · Mathematics 2020-08-18 Leqi Chen , Shuang Chen

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

This paper investigates the large time behaviour of a three species reaction-diffusion system, modelling the spatial invasion of two predators feeding on a single prey species. In addition to the competition for food, the two predators…

Analysis of PDEs · Mathematics 2020-07-07 Arnaud Ducrot , Thomas Giletti , Jong-Shenq Guo , Masahiko Shimojo

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