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We present properties of Lotka-Volterra equations describing ecological competition among a large number of competing species. First we extend to the case of a non-homogeneous niche space stability conditions for solutions representing…

A diffusive Lotka-Volterra competition model is considered for the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion. First it is shown that in a two-species system in which…

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…

We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we…

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…

We study a parabolic Lotka-Volterra type equation that describes the evolution of a population structured by a phenotypic trait, under the effects of mutations and competition for resources modelled by a nonlocal feedback. The limit of…

The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these…

This paper is concerned with a nonlocal diffusion Lotka-Volterra type competition model that consisting of a native species and an invasive species in a one-dimensional habitat with free boundaries. We prove the well-posedness of the system…

Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We…

We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a…

We study the properties of Lotka-Volterra competitive models in which the intensity of the interaction among species depends on their position along an abstract niche space through a competition kernel. We show analytically and numerically…

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…

In this work we consider three species competing with each other in the same habitat. One of the species lives in the entire habitat, competing with the other two species, while the other two inhabit two disjoint regions of the habitat.…

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…

Bacteria regulate their motility through a variety of mechanisms, including quorum sensing (QS) and other density-dependent responses mediated by diffusible signals. While nonlinear density-dependent motility is well known in active-matter…

This paper deals with coexistence and extinction of time periodic Volterra-Lotka type competing systems with nonlocal dispersal. Such issues have already been studied for time independent systems with nonlocal dispersal and time periodic…

We investigate the competing effects and relative importance of intrinsic demographic and environmental variability on the evolutionary dynamics of a stochastic two-species Lotka-Volterra model by means of Monte Carlo simulations on a…

We study the fixation probability of a mutant type when introduced into a resident population. As opposed to the usual assumption of constant pop- ulation size, we allow for stochastically varying population sizes. This is implemented by a…

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…

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…