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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…
We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we…
We study communities emerging from generalised random Lotka--Volterra dynamics with a large number of species with interactions determined by the degree of niche overlap. Each species is endowed with a number of traits, and competition…
We study the equilibria of a large Lokta-Volterra system of coupled differential equations in the case where the interaction coefficients form a large random matrix. In the case where this random matrix follows an elliptic model , we study…
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…
We investigate a class of models for opinion dynamics in a population with two interacting families of individuals. Each family has an intrinsic mean field "Voter-like" dynamics which is influenced by interaction with the other family. The…
The Lotka-Volterra system is a set of ordinary differential equations describing growth of interacting ecological species. This model has gained renewed interest in the context of random interaction networks. One of the debated questions is…
In complex ecological communities, species may self-organize into clusters or clumps where highly similar species can coexist. The emergence of such species clusters can be captured by the interplay between neutral and niche theories. Based…
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…
The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive…
When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…
In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka-Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by…
We investigate the Multiple Equilibria phase of generalized Lotka-Volterra dynamics with random, non-reciprocal interactions. We compute the topological complexity of equilibria, which quantifies how rapidly the number of equilibria of the…
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…
Spatial evolution is investigated in a simulated system of nine competing and mutating bacterium strains, which mimics the biochemical war among bacteria capable of producing two different bacteriocins (toxins) at most. Random sequential…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
The Lotka-Volterra (LV) model is a simple, robust, and versatile model used to describe large interacting systems such as food webs or microbiomes. The model consists of $n$ coupled differential equations linking the abundances of $n$…
In this paper we are investigating the long time behaviour of the solution of a mutation competition model of Lotka-Volterra's type. Our main motivation comes from the analysis of the Lotka-Volterra's competition system with mutation which…
Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…
We study some aspects of the global dynamics of an $n$-dimensional Lotka-Volterra system with infinite delay and patch structure, such as extinction, persistence, existence and global attractivity of a positive equilibrium. Both the cases…