Fanni Sélley: Coupled map systems with a continuum of sites

Speaker: Fanni Sélley

Title: Coupled map systems with a continuum of sites

Abstract: Coupled map systems are simple models of a finite or infinite network of interacting units. It is convenient to think of the network as an undirected graph, with a site located at each node modeled by a discrete time dynamical system. The dynamics of the compound system is given by the composition of the (typically chaotic) individual dynamics and a coupling map representing the characteristics of the interaction. The coupling map usually includes a parameter 0 ≤ ε ≤ 1, representing the strength of interaction along the edges of the network graph. The main interest in such models lies in the emergence of bifurcations when ε is varied. We first introduce our results for small finite systems. Then we initiate a new point of view which focuses on the evolution of distributions and allows to incorporate the investigation of a continuum of sites.