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We study a class of elliptic competition-diffusion systems of long range segregation models for two and more competing species. The existence and uniqueness of the solution are shown. We prove that as the competition rate goes to infinity…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
A microscopic agent dynamical model for diploid age-structured populations is used to study evolution of polymorphism and sympatric speciation. The underlying ecology is represented by a unimodal distribution of resources of some width.…
In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time…
We model the growth, dispersal and mutation of two phenotypes of a species using reaction-diffusion equations, focusing on the biologically realistic case of small mutation rates. After verifying that the addition of a small linear mutation…
In this article, we are interested in a non-monotone system of logistic reaction-diffusion equations. This system of equations models an epidemics where two types of pathogens are competing, and a mutation can change one type into the other…
How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though…
Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al.,…
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…
In this article, we investigate a competitive reaction-diffusion system modelling the interaction between several species of mosquitoes. In particular, it has been observed that in tropical regions, Aedes aegypti mosquitoes are well…
In order to understand how impulsive interventions and environmental perturbations affect dynamics of competitors, we focus on a diffusive competition model with free boundaries and periodic pulses in a temporally heterogeneous environment…
It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…
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…
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…
Spatially periodic reaction-diffusion equations typically admit pulsating waves which describe the transition from one steady state to another. Due to the heterogeneity, in general such an equation is not invariant by rotation and therefore…
A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing…
Interactions among multiple infectious agents are increasingly recognized as a fundamental issue in the understanding of key questions in public health, regarding pathogen emergence, maintenance, and evolution. The full description of…
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…
In relation to spatiotemporal intermittency, as it can be observed in coupled map lattices, we study the stability of different wavelengths in competition. Introducing a two dimensional map, we compare its dynamics with the one of the whole…
This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover…