Related papers: The diffusive competition problem with a free boun…
In this paper we investigate a free boundary problem for a predator-prey model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the free boundaries…
In this paper we study a ratio-dependent predator-prey model with a free boundary causing by both prey and predator over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing…
We investigate how initial and boundary conditions influence the competition dynamics and outcome in dispersal-structured populations. The study is carried out through numerical modeling of the heterogeneous Brownian bugs model, in which…
The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic…
The paper is concerned with different types of dispersal chosen by competing species. We introduce a model with the diffusion-type term $\nabla \cdot \left[ a \nabla \left( u/P \right) \right]$ which includes some previously studied systems…
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…
We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann…
It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…
We study the propagation speed of bistable traveling waves in the classical two-component diffusive Lotka-Volterra system under strong competition. From an ecological perspective, the sign of the propagation speed determines the long-term…
We study a discrete spatial model for invasive allele spread in which two alleles compete preemptively, initially only the "residents" (weaker competitors) being present. We find that the spread of the advantageous mutation is well…
How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…
Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…
Population survival depends on a large set of factors that includes environment structure. Due to landscape heterogeneity, species can occupy particular regions that provide the ideal scenario for development, working as a refuge from…
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-\Delta u=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\in\Omega,\nonumber \end{equation} where $\Omega$ is of…
We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the…
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…
Invasion phenomena for heterogeneous reaction-diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction-diffusion equation when the…