Related papers: Influence of density-dependent diffusion on patter…
We take interest in a reaction-diffusion system which has been recently proposed [11] as a model for the effect of a road on propagation phenomena arising in epidemiology and ecology. This system consists in coupling a classical Fisher-KPP…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…
In Cao, Du, Li and Li [8], a nonlocal diffusion model with free boundaries extending the local diffusion model of Du and Lin [12] was introduced and studied. For Fisher-KPP type nonlinearities, its long-time dynamical behaviour is shown to…
Social dilemmas concern a natural conflict between cooperation and self interests among individuals in large populations. The emergence of cooperation and its maintenance is the key for the understanding of fundamental concepts about the…
An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…
In this paper, based on the epidemiological microparasite model, a parasite-host model is established by considering the fear effect of susceptible individuals on infectors. We explored the pattern formation with the help of numerical…
Actively propelled particles undergoing dissipative collisions are known to develop a state of spatially distributed coherently moving clusters. For densities larger than a characteristic value clusters grow in time and form a stationary…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
We introduce a non-diffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent…
The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…
Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
We investigate the random close packing density, $\phi_\textrm{RCP}$, of polydisperse hard sphere systems using a theoretical framework based on the equilibrium model of crowding. We derive a closed-form solution for $\phi_\textrm{RCP}$ in…
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial…
We study a spatial predator-prey model in which prey can enter a protection zone (refuge) inaccessible to predators, while predators exhibit directed movement toward prey-rich regions. The directed movement is modeled by a far-sighted…
The Fisher-KPP equation is a model for population dynamics that has generated a huge amount of interest since its introduction in 1937. The speed with which a population spreads has been computed quite precisely when the initial data decays…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
In order to understand how nonlocal diffusion and pulse intervention affect dynamics of species, we focus on an age-structured nonlocal diffusion model in moving and heterogeneous environment, where nonlocal diffusion describes the long…