Low-dimensional chaos in populations of strongly-coupled noisy maps

We characterize the macroscopic attractor of infinite populations of noisy maps subjected to global and strong coupling by using an expansion in order parameters. We show that for any noise amplitude there exists a large region of strong coupling where the macroscopic dynamics exhibits low-dimensional chaos embedded in a hierarchically-organized, folded, infinite-dimensional set. Both this structure and the dynamics occuring on it are well-captured by our expansion. In particular, even low-degree approximations allow to calculate efficiently the first macroscopic Lyapunov exponents of the full system.