Related papers: Influence of density-dependent diffusion on patter…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
We study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the…
Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to…
Starting from an age-structured diffusive population growth law for single species in a discrete and periodic habitat, we formulate a stage structured population model with spatially periodic dispersal, mortality and recruitment. With a KPP…
Population dynamics is constrained by the environment, which needs to obey certain conditions to support population growth. We consider a standard model for the evolution of a single species population density, that includes reproduction,…
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…
How do interactions between species influence their spatial distribution in an ecosystem? To answer this question, we introduce a spatially-extended ecosystem of Generalized Lotka-Volterra type, where species can diffuse and interactions…
Fitness consequence of dispersal depends on property of the entire landscape, which patches are available and what are the cost of moving. These are information that are not available locally when an organism make the decision to disperse.…
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…
We investigate how environmental flows influence spatial pattern formation and population dynamics using two nonlocal models of population dynamics, which we couple to two different stationary flows. Combining numerical simulations and…
We investigate the asymptotic speed of spread of the solutions of a non-autonomous Fisher-KPP equation with nonlocal diffusion, driven by a thin-tailed kernel. In this paper, we are concerned with both compactly supported and exponentially…
This paper is concerned with spreading properties of space-time heterogeneous Fisher--KPP equations in one space dimension. We focus on the case of everywhere favorable environment with three different zones, a left half-line with slow or…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
In this paper, a single population model with memory effect and the heterogeneity of the environment, equipped with the Neumann boundary, is considered. The global existence of a spatial nonhomogeneous steady state is proved by the method…
The purpose of the current paper is to unveil the key mechanism which is responsible for the occurrence of {\it Turing-type instability} for a non-local Fisher-KPP type model. In particular, we prove that the solution of the considered…
We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a L\'{e}vy dust, which allows…
In this paper, we investigate a Fisher-KPP nonlocal diffusion model incorporating the effect of advection and free boundaries, aiming to explore the propagation dynamics of the nonlocal diffusion-advection model. Considering the effects of…
Advection of entities induced by gradients in attractant concentration fields is observed via diffusiophoresis in colloids and via chemotaxis in microorganisms. Mathematically, both diffusiophoresis and chemotaxis follow similar…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…