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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.Comment: 16 pages, 9 figures. Progress of Theoretical Physics, to appea
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