1 citations · 1 across the 5 of their papers we have counts for
7 papers
Heteroclinic cycles and long-time behavior in a singularly perturbed three-species Lotka--Volterra system
Arnaud Ducrot, Quentin Griette, Quang-Vinh Tran
We study a three-species competitive Lotka--Volterra system with cyclic dominance, motivated by rock--paper--scissors interactions in ecological communities. The model contains a s…
On advective nonlocal operators: multiplicity of principal eigenpairs
Arnaud Ducrot, Quentin Griette, Xing Liang
We study the existence and multiplicity of principal eigenvalues and eigenfunctions for a periodically heterogeneous nonlocal dispersal model with advection. The operator we consid…
Front propagation into unstable states for periodic monotone reaction-diffusion systems
Liangliang Deng, Arnaud Ducrot, Quentin Griette
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that con…
Traveling wave solutions and spreading speeds for a scalar age-structured equation with nonlocal diffusion
Arnaud Ducrot, Hao Kang
In this paper, we study the existence of traveling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs…
Age-structured Models with Nonlocal Diffusion of Dirichlet Type, I: Principal Spectral Theory and Limiting Properties
Arnaud Ducrot, Hao Kang, Shigui Ruan
Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in wh…
Sharp interface limit of the Fisher-KPP equation when initial data have slow exponential decay
Matthieu Alfaro, Arnaud Ducrot
We investigate the singular limit, as $\ep \to 0$, of the Fisher equation $\partial_t u=\ep Δu + \ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support…