Related papers: Nonlinear diffusion effects on biological populati…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of…
Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain…
In this paper, we investigate the effect of dispersal and advection on the dynamics of a predator-prey model. More precisely, we show that the linear stability of the semi-trivial steady state is determined by the dispersal rate, the…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
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 decompose the anomalous diffusive behavior found in a model of aging into its fundamental constitutive causes. The model process is a sum of increments that are iterates of a chaotic dynamical system, the Pomeau-Manneville map. The…
This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…
We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is non-local, and show that spatial structures with interesting…
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…
This work studies a nonlocal extension of the Klausmeier vegetation model in $\mathbb{R}^N$ $(N \ge 1)$ that incorporates both local and nonlocal diffusion. The biomass dynamics are driven by a nonlocal convolution operator, representing…
Establishing the conditions that guarantee the spreading or the sustenance of altruistic traits in a population is the main goal of intergroup selection models. Of particular interest is the balance of the parameters associated to group…
Diffusion models generate samples by incrementally reversing a process that turns data into noise. We show that when the step size goes to zero, the reversed process is invariant to the distribution of these increments. This reveals a…
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…
Intraspecific trait variation has been increasingly recognized as an important factor in determining species interaction and diversity. Eco-evolutionary models have studied the distribution of trait values within a population that changes…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
In this paper, we are concerned with a two-species competitive model with diffusive terms on a periodically evolving domain and study the impact of the spatial periodic evolution on the dynamics of the model. The Lagrangian transformation…
Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the…