Related papers: Competition in periodic media: I -- Existence of p…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
This paper explains the uniqueness of positive steady state of general Lotka-Volterra competition model of two species of animals in the same environment.
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…