Estimation of stationary measure for mean field coupled systems

Speaker:  Dr Maxence Phalempin 
Affiliation: UNSW, Sydney

Abstract

A mean-field coupled system is a model of a large collection of dynamical systems where the dynamics of each of them is perturbed through an averaged interaction with the states of the remaining systems in that collection. Methods have been developed to study stationary measures for such coupled dynamical systems that rely on fixed-point theorems and the behavior of cocycles generated by a nonlinear “transfer” operator. However, these methods and the non-linearity of that operator rule out the explicit identification of such stationary measures and the use of the classical Ulam method to estimate them. In this talk, I will present some methods to estimate the invariant measure in mean-field coupled systems.