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This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. Parameters in the model are modified so that each of them…

Dynamical Systems · Mathematics 2012-11-27 Hanbaek Lyu , Piotr Grzegorz Jablonski

In this note we present a study of the solutions associated to a particular spatial extension of the Rosenzweig-MacArthur model for predator and prey. The analysis presented here shows that positive steady state solutions emerge via a…

Dynamical Systems · Mathematics 2021-03-15 Leoncio Rodriguez Quinones , Luis F. Gordillo

Spatial heterogeneity and habitat characteristic are shown to determine the asymptotic profile of the solution to a reaction-diffusion model with free boundary, which describes the moving front of the invasive species. A threshold value…

Analysis of PDEs · Mathematics 2014-03-26 Chengxia Lei , Zhigui Lin , Qunying Zhang

In this paper, we study the Lotka-Volterra prey-predator models consisting of two species on finite connected graphs under Neumann condition and the condition that there is no boundary condition. We establish the global stability of the…

Analysis of PDEs · Mathematics 2022-12-15 Yuanyang Hu , Chengxia Lei

We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two adjacent populations: each population undergoes linear diffusion and logistic growth, and the boundary between…

Populations and Evolution · Quantitative Biology 2023-09-06 Matthew J Simpson , Nizhum Rahman , Scott W McCue , Alexander KY Tam

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 concerns a diffusive logistic equation with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, in which the variable intrinsic growth rate may be "very negative" in a "suitable…

Analysis of PDEs · Mathematics 2015-09-22 Mingxin Wang

The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing…

Analysis of PDEs · Mathematics 2020-02-05 Félix del Teso , Jørgen Endal , Juan Luis Vázquez

A non-periodic version of the one-predator two-prey system model presented in [L.T.H. Nguyen, Q.H. Ta, T.V. T\d{a}, Existence and stability of periodic solutions of a Lotka-Volterra system, SICE International Symposium on Control Systems,…

Dynamical Systems · Mathematics 2017-09-12 Linh Thi Hoai Nguyen , Quang Hong Ta , Ton Viet Ta

We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, where humans get infected by the agents, and…

Analysis of PDEs · Mathematics 2019-12-06 Meng Zhao , Yang Zhang , Wan-Tong Li , Yihong Du

Following the well-extablished mathematical approach to persistence and its recent developments we give a rigorous theoretical explanation to the numerical results obtained for a certain prey-predator model with functional response of…

Dynamical Systems · Mathematics 2019-01-23 Tobia Dondè

We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…

Analysis of PDEs · Mathematics 2019-07-08 Arnaud Ducrot , Thomas Giletti , Hiroshi Matano

We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a spherically symmetric setting. This free boundary…

Analysis of PDEs · Mathematics 2015-06-19 Yihong Du , Mingxin Wang , Maolin Zhou

We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…

Analysis of PDEs · Mathematics 2022-12-06 Henri Berestycki , Alessandro Zilio

A diffusive predator-prey system with predator interference and Neumann boundary conditions is considered in this paper. We derive some results on the existence and nonexistence of nonconstant stationary solutions. It is shown that there…

Dynamical Systems · Mathematics 2017-01-11 Shanshan Chen , Junjie Wei , Jinzhu Yu

This paper focus on the diffusive eco-epidemiological prey-predator model with infectious diseases in prey, and with the homogeneous Neumann and Dirichlet boundary conditions, respectively. When boundary conditions are homogeneous Neumann…

Analysis of PDEs · Mathematics 2022-11-08 Mingxin Wang

An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is considered. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence…

Analysis of PDEs · Mathematics 2010-02-10 Christoph Walker

The goal of this work is to explain an unexpected feature of the expanding level sets of the solutions of a system where a half plane, in which reaction-diusion phenomena take place, exchanges mass with a line having a large diusion of its…

Analysis of PDEs · Mathematics 2019-03-15 Luis Caffarelli , Jean-Michel Roquejoffre

This paper concerns the effect of the (separated/connected) protection zone for the evolution of an endangered species on the reaction-diffusion equation with strong Allee effect and free boundary. We give a description of the long-time…

Analysis of PDEs · Mathematics 2021-08-04 Ningkui Sun , Chengxia Lei

The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…

Statistical Mechanics · Physics 2011-06-02 Rakesh Chatterjee , P. K. Mohanty , Abhik Basu