相关论文: Spreading in a shifting environment modeled by the…

An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…

The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a…

We investigate the spreading properties of a three-species competition-diffusion system, which is non-cooperative. We apply the Hamilton-Jacobi approach, due to Freidlin, Evans and Souganidis, to establish upper and lower estimates of…

Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…

When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic…

The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…

We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…

This paper concerns the free boundary problem of an epidemic model. The spatial movements of the infectious agents and the infective humans are approximated by nonlocal diffusion operators. Especially, both the growth rate of the agents and…

Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…

This paper is devoted to the study of persistence and extinction of a species modeled by nonlocal dispersal evolution equations in moving habitats with moving speed $c$. It is shown that the species becomes extinct if the moving speed $c$…

Many species see their range shifted poleward in response to global warming and need to keep pace in order to survive. To understand the effect of climate change on species ranges and its consequences on population dynamics, we consider a…

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…

Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…

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…

Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…

This paper is concerned with the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators, and the epidemic region is represented by an evolving interval…

The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…

We examine the two-dimensional extension of the model of Kessler and Sander of competition between two species identical except for dispersion rates. In this class of models, the spatial inhomogeneity of reproduction rates gives rise to an…

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…

A reaction-diffusion-advection model is proposed and investigated to understand the invasive dynamics of Aedes aegypti mosquitoes. The free boundary is introduced to model the expanding front of the invasive mosquitoes in a heterogenous…