Related papers: On a reaction-diffusion system modeling strong com…
We analysed some qualitative properties of the limit configuration of the solutions of a reaction-diffusion system of four competing species as the competition rate tends to infinity. Large interaction induces the spatial segregation of the…
We introduce a stochastic individual model for the spatial behavior of an animal population of dispersive and competitive species, considering various kinds of biological effects, such as heterogeneity of environmental conditions, mutual…
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…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the…
Mosquito-borne diseases cause significant public health burden, mostly in tropical and sub-tropical regions, and are widely emerging or re-emerging in areas where previously absent. Understanding, predicting, and mitigating the spread of…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…
Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively…
In this work we develop a discrete model of competing species affected by a common parasite. We analyze the influence of the fast development of the shared disease on the community dynamics. The model is presented under the form of a two…
Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global…
We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space…
Arboviral diseases remain a major public health concern, particularly in tropical and subtropical regions where mosquito populations thrive. One promising strategy to curb transmission is the release of Aedes aegypti mosquitoes infected…
We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…
Mosquito-borne diseases cause several hundred thousand deaths every year. Deciphering mosquito host-seeking behavior is essential to prevent disease transmission through mosquito capture and surveillance. Despite recent substantial…
We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…
Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generality. The present paper focuses on the simplest mathematical…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
We present a simple model based on a reaction-diffusion equation to explain pattern formation in a multicellular bacterium (Streptomyces). We assume competition for resources as the basic mechanism that leads to pattern formation; in…
We study a chemotaxis system that includes two competitive prey and one predator species in a two-dimensional domain, where the movement of prey (resp. predators) is driven by chemicals secreted by predators (resp. prey), called mutually…
This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trival steady state for the…