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This paper is concerned with a Lotka-Volterra type competition model with free boundaries in time-periodic environment. One species is assumed to adopt nonlocal dispersal and the other one adopts mixed dispersal, which is a combination of…

Analysis of PDEs · Mathematics 2021-01-21 Qiaoling Chen , Fengquan Li , Sanyi Tang , Feng Wang

We investigate the controllability of the competition-diffusion Lotka-Volterra system. Our primary focus is on the one-dimensional setting with Dirichlet boundary controls, interpreted as ecological management policies regulating the…

Analysis of PDEs · Mathematics 2025-08-04 Elisa Affili , Enrique Zuazua

This paper is concerned with the asymptotic spreading behavior of solutions of the Lotka-Volterra system with strong competition in $\mathbb{R}^{N}$. Two types of initial conditions are proposed: (C1) two species initially occupy bounded…

Analysis of PDEs · Mathematics 2024-11-22 Hui Bao , Hongjun Guo

In this paper, we consider the phenomenon of monostable pulsating fronts for multi-dimensional reaction-diffusion-advection systems in periodic media. Recent results have addressed the existence of pulsating fronts and the linear…

Analysis of PDEs · Mathematics 2025-04-29 Li-Jun Du , Wan-Tong Li , Ming-Zhen Xin

This paper deals with coexistence and extinction of time periodic Volterra-Lotka type competing systems with nonlocal dispersal. Such issues have already been studied for time independent systems with nonlocal dispersal and time periodic…

Dynamical Systems · Mathematics 2016-08-30 Tung Nguyen , Nar Rawal

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 pulsating travelling fronts for a KPP reaction-diffusion equation posed in a multi-dimensional periodic medium. We provide an alternative proof of the classic existence result. Our proof relies…

Analysis of PDEs · Mathematics 2023-03-16 Liangliang Deng , Arnaud Ducrot

We devote this paper to the issue of existence of pulsating travelling front solutions for spatially periodic heterogeneous reaction-diffusion equations in arbitrary dimension, in both bistable and more general multistable frameworks. In…

Analysis of PDEs · Mathematics 2019-01-23 Thomas Giletti , Luca Rossi

This paper investigates the bistable traveling waves for two-species Lotka-Volterra competition systems in time periodic environments. We focus especially on the influence of the temporal period, with existence results established for both…

Analysis of PDEs · Mathematics 2025-09-17 Weiwei Ding , Zhanghua Liang

The Lotka--Volterra competition system with diffusion is considered. The Painlev\'e property of this system is investigated. Exact traveling wave solutions of the Lotka--Volterra competition system are found. Periodic solutions expressed in…

Exactly Solvable and Integrable Systems · Physics 2014-09-25 Nikolay A. Kudryashov , Anastasia S. Zakharchenko

We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Dirichlet boundary conditions. For a class of nonconvex domains composed by balls connected with thin corridors, we show the occurrence of pattern…

Analysis of PDEs · Mathematics 2007-12-06 Monica Conti , Veronica Felli

This paper studies the spreading dynamics of a high-dimensional strong competition Lotka-Volterra system where two species initially occupy disjoint measurable (possibly unbounded) subsets in $\mathbb{R}^N$, which are called initial…

Analysis of PDEs · Mathematics 2026-02-26 Hongjun Guo

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

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

We investigate traveling wave solutions in the two-species reaction-diffusion Lotka-Volterra competition system under weak competition. For the strict weak competition regime $(b<a<1/c,\,d>0)$, we construct refined upper and lower solutions…

Analysis of PDEs · Mathematics 2026-03-26 Chiun-Chuan Chen , Ting-Yang Hsiao , Shun-Chieh 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

We consider the reaction-diffusion competition system in the so-called {\it critical competition case}. The associated ODE system then admits infinitely many equilibria, which makes the analysis intricate. We first prove the non-existence…

Analysis of PDEs · Mathematics 2021-10-01 Matthieu Alfaro , Dongyuan Xiao

This paper is concerned with a diffusive Lotka-Volterra type competition system with a free boundary in one space dimension. Such a system may be used to describe the invasion of a new species into the habitat of a native competitor. We…

Analysis of PDEs · Mathematics 2017-10-17 Zhiguo Wang , Hua Nie , Yihong Du

This paper explains the uniqueness of positive steady state of general Lotka-Volterra competition model of two species of animals in the same environment.

Analysis of PDEs · Mathematics 2008-06-24 Joon Hyuk Kang

We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…

Analysis of PDEs · Mathematics 2015-05-28 Chunyi Gai , Qi Wang , Jingda Yan