18 citations · 43 across the 13 of their papers we have counts for
16 papers
Neural Field Equations and Hawkes processes: long-term stability of traveling wave profiles in the neutral case
Eric Luçon, Christophe Poquet
We consider the long-time behavior of a population of interacting Hawkes processes on the real line, with spatial extension. The large population behavior of the system is governed…
A note on uniform in time mean-field limit in graphs
Pierre Le Bris, Christophe Poquet
In this article we show, in a concise manner, a result of uniform in time propagation of chaos for non exchangeable systems of particles interacting according to a random graph. Pr…
Central Limit Theorems for global and local empirical measures of diffusions on Erdős-Rényi graphs
Fabio Coppini, Eric Luçon, Christophe Poquet
We address the issue of the Central Limit Theorem for (both local and global) empirical measures of diffusions interacting on a possibly diluted Erdős-Rényi graph. Special attentio…
Periodicity and longtime diffusion for mean field systems in
Eric Luçon, Christophe Poquet
We study in this paper the longtime behavior of some large but finite populations of interacting stochastic differential equations whose (infinite population) limit Fokker-Planck P…
Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations
Eric Luçon, Christophe Poquet
We consider a class of nonlinear Fokker-Planck equations describing the dynamics of an infinite population of units within mean-field interaction. Relying on a slow-fast viewpoint…
Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh-Nagumo model
Eric Luçon, Christophe Poquet
We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in large population. Each neuron is represented…
Emergence of oscillatory behaviors for excitable systems with noise and mean-field interaction, a slow-fast dynamics approach
Eric Lucon, Christophe Poquet
We consider the long-time dynamics of a general class of nonlinear Fokker-Planck equations, describing the large population behavior of mean-field interacting units. The main motiv…
Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems
Jacopo de Simoi, Carlangelo Liverani, Christophe Poquet +1
We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wen…
On the relaxation rate of short chains of rotors interacting with Langevin thermostats
Noé Cuneo, Christophe Poquet
In this short note, we consider a system of two rotors, one of which interacts with a Langevin heat bath. We show that the system relaxes to its invariant measure (steady state) no…
Small noise and long time phase diffusion in stochastic limit cycle oscillators
Giambattista Giacomin, Christophe Poquet, Assaf Shapira
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is pe…
Long time behavior of Markov processes and beyond
Florian Bouguet, Florent Malrieu, Fabien Panloup +2
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, p…
Long time dynamics and disorder-induced traveling waves in the stochastic Kuramoto model
Eric Luçon, Christophe Poquet
The aim of the paper is to address the long time behavior of the Kuramoto model of mean-field coupled phase rotators, subject to white noise and quenched frequencies. We analyse th…
Phase Reduction in the Noise Induced Escape Problem for Systems close to Reversibility
Christophe Poquet
We consider n-dimensional deterministic flows obtained by perturbing a gradient flow. We assume that the gradient flow admits a stable curve of stationary points, and thus if the p…
Synchronization and random long time dynamics for mean-field plane rotators
Lorenzo Bertini, Giambattista Giacomin, Christophe Poquet
We consider the natural Langevin dynamics which is reversible with respect to the mean-field plane rotator (or classical spin XY) measure. It is well known that this model exhibits…
Coherence stability and effect of random natural frequencies in populations of coupled oscillators
Giambattista Giacomin, Eric Luçon, Christophe Poquet
We consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequen…
Transitions in active rotator systems: invariant hyperbolic manifold approach
Giambattista Giacomin, Khashayar Pakdaman, Xavier Pellegrin +1
Our main focus is on a general class of active rotators with mean field interactions, that is globally coupled large families of dynamical systems on the unit circle with non-trivi…