Related papers: Global dynamics of the chemostat with variable yie…
Population dynamics are often affected by sudden environmental perturbations. Parameters of stochastic models are often imprecise due to various uncertainties. In this paper, we formulate a stochastic Lotka Volterra food chain chemostat…
Ecological trade-offs between species are often invoked to explain species coexistence in ecological communities. However, few mathematical models have been proposed for which coexistence conditions can be characterized explicitly in terms…
The global asymptotic behavior of the classical diffusive Lotka-Volterra competition model with stage structure is studied. A complete classification of the global dynamics is given for the weak competition case. It is shown that under…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Using the Lyapunov criteria arguments, we find sufficient conditions on explosion/nonexplosion for continuous-state branching processes with competition in L\'evy random environment. In particular, we identify the necessary and sufficient…
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…
In apparent contradiction to competition theory, the number of known, co-existing plankton species far exceeds their explicable biodiversity - a discrepancy termed the Paradox of the Plankton. We introduce a new game-theoretic model for…
We study a competitive infection-age structured SI model between two diseases. The well-posedness of the system is handled by using integrated semigroups theory, while the existence and the stability of disease-free or endemic equilibria…
In this paper, we study the global dynamics of a general $2\times 2$ competition models with nonsymmetric nonlocal dispersal operators. Our results indicate that local stability implies global stability provided that one of the diffusion…
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some…
In this work, we study a model of the chemostat where the species are present in two forms, isolated bacteria and under an aggregated form like attached bacteria or bacteria in flocks. We show that our general model contains a lot of models…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
Virtually every biological function emerges through the organization of molecules in time and space. Consequently, a major challenge in statistical physics is to uncover the universal principles governing macromolecular self-organization…
We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio…
This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…
Environmental fluctuations have important consequences in the organization of ecological communities, and understanding how such a variability influences the biodiversity of an ecosystem is a major question in ecology. In this paper, we…
Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime…
Microbial populations generally evolve in volatile environments, under conditions fluctuating between harsh and mild, e.g. as the result of sudden changes in toxin concentration or nutrient abundance. Environmental variability thus shapes…