61 citations · 123 across the 15 of their papers we have counts for
17 papers
Persistence, extinction and spreading properties of non-cooperative Fisher--KPP systems in space-time periodic media
Léo Girardin
This paper is concerned with asymptotic persistence, extinction and spreading properties for non-cooperative Fisher-KPP systems with space-time periodic coefficients. Results are f…
Pulled, pushed or failed: the demographic impact of a gene drive can change the nature of its spatial spread
Léna Kläy, Léo Girardin, Vincent Calvez +1
Understanding the temporal spread of gene drive alleles -- alleles that bias their own transmission -- through modeling is essential before any field experiments. In this paper, we…
Agro-ecological control of a pest-host system: preventing spreading
Léo Girardin, Baptiste Maucourt
We consider an agro-ecologically motivated coupling between a prey-predator system and a vector-borne epidemic system. The coupled system contains one ODE, two reaction-diffusion P…
Generalized principal eigenvalues of space-time periodic, weakly coupled, cooperative, parabolic systems
Léo Girardin, Idriss Mazari
This paper is concerned with generalizations of the notion of principal eigenvalue in the context of space-time periodic cooperative systems. When the spatial domain is the whole s…
A note on "Existence and uniqueness of coexistence states for an elliptic system coupled in the linear part", by Hei Li-Jun, Nonlinear Anal. Real World Appl. 5, 2004
Léo Girardin
In this short paper I report on a paper published in Nonlinear Analysis: Real World Applications in 2004. There is a major mistake early in that paper which makes most of its claim…
Demographic feedbacks can hamper the spatial spread of a gene drive
Léo Girardin, Florence Débarre
This paper is concerned with a reaction--diffusion system modeling the fixation and the invasion in a population of a gene drive (an allele biasing inheritance, increasing its own…
Spatial segregation limit of traveling wave solutions for a fully nonlinear strongly coupled competitive system
Léo Girardin, Danielle Hilhorst
The paper is concerned with a singular limit for the bistable traveling wave problem in a very large class of two-species fully nonlinear parabolic systems with competitive reactio…
When the Allee threshold is an evolutionary trait: persistence vs. extinction
Matthieu Alfaro, Léo Girardin, Francois Hamel +1
We consider a nonlocal parabolic equation describing the dynamics of a population structured by a spatial position and a phenotypic trait, submitted to dispersion , mutations and g…
A Liouville-type result for non-cooperative Fisher--KPP systems and nonlocal equations in cylinders
Léo Girardin, Quentin Griette
We address the uniqueness of the nonzero stationary state for a reaction-diffusion system of Fisher-KPP type that does not satisfy the comparison principle. Although the uniqueness…
The effect of random dispersal on competitive exclusion -- A review
Léo Girardin
Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generalit…
Two components is too simple: an example of oscillatory Fisher--KPP system with three components
Léo Girardin
In a recent paper by Cantrell, Cosner and Yu, two-component KPP systems with competition of Lotka--Volterra type were analyzed and their long-time behavior largely settled. In part…
Competition in periodic media: III -- Existence \& stability of segregated periodic coexistence states
Léo Girardin, Alessandro Zilio
In this paper we consider a system of parabolic reaction-diffusion equations with strong competition and two related scalar reaction-diffusion equations. We are mainly concerned wi…
Invasion of open space by two competitors: spreading properties of monostable two-species competition--diffusion systems
Léo Girardin, King-Yeung Lam
This paper is concerned with some spreading properties of monostable Lotka--Volterra two-species competition--diffusion systems when the initial values are null or exponentially de…
Non-cooperative Fisher--KPP systems: traveling waves and long-time behavior
Léo Girardin
This paper is concerned with non-cooperative parabolic reaction--diffusion systems which share structural similarities with the scalar Fisher--KPP equation. These similarities make…
Competition in periodic media: II -- Segregative limit of pulsating fronts and "Unity is not Strength"-type result
Léo Girardin, Grégoire Nadin
This paper is concerned with the limit, as the interspecific competition rate goes to infinity, of pulsating front solutions in space-periodic media for a bistable two-species comp…
Competition in periodic media: I -- Existence of pulsating fronts
Léo Girardin
This paper is concerned with the existence of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. Considerin…
Travelling waves for diffusive and strongly competitive systems: relative motility and invasion speed
Léo Girardin, Grégoire Nadin
Our interest here is to find the invader in a two species, diffusive and competitive Lotka-Volterra system in the particular case of travelling wave solutions. We investigate the r…