Related papers: Selected topics on reaction-diffusion-advection mo…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
In this paper, we study a diffusive Lotka-Volterra competition model under homogeneous Dirichlet boundary conditions. We shall discuss the effects of dispersal rate and spatial heterogeneity on population dynamics. More precisely, we…
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…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
In this paper, we study a three-patch two-species Lotka-Volterra competition patch model over a stream network. The individuals are subject to both random and directed movements, and the two species are assumed to be identical except for…
We study the limit of many small mutations of a model of population dynamics. The population is structured by phonological traits and is spatially inhomogeneous. The various sub-populations compete for the same nutrient which diffuses…
We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one of the effects…
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map…
This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
In this study, a spatially distributed reaction-diffusion-advection (RDA) model with harvesting is investigated to signify the outcome of a competition between two competing species in a heterogeneous environment. The study builds upon the…
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
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…
The growth and evolution of microbial populations is often subjected to advection by fluid flows in spatially extended environments, with immediate consequences for questions of spatial population genetics in marine ecology, planktonic…
Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…
We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
We investigate the global dynamics of a special case of the classical Lotka-Volterra competition-diffusion system in spatially heterogeneous environment. This model indicates that the evolution of the density of the predator is independent…
This paper is devoted to the analysis of a reaction-diffusion system with strong competition and spatial heterogeneities modelling the interaction between two species of mosquitoes. In particular, we propose a mathematical model that…