Coupled Chaotic Maps and Self-Consistent Transfer Operators

Date: Thursday 3rd April 2025

Abstract

At the end of the 1980s, globally coupled maps (GCMs) emerged as high-dimensional models for complex systems. These models feature simple equations where several variables are coupled symmetrically all-to-all, and display a rich variety of behaviors, including synchronization, phase ordering, and turbulence. Rigorous mathematical studies of the dynamics of GCMs have primarily focused on their mean-field limit—that is, the behavior of the system’s average state as the number of maps approaches infinity. This limit is governed by a nonlinear operator known as the self-consistent transfer operator, which dictates the evolution of the mean field. In this talk, I will provide a brief overview of the origin of the study of self-consistent transfer operators and discuss some recent progress in the field focusing on coupled chaotic maps.