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The affect of demographic stochasticity of a system of globally coupledchaotic maps is considered. A two-step model is studied, where the intra-patchchaotic dynamics is followed by a migration step that coupled all patches; theequilibrium number of agents on each site, $N$, controls the strength of thediscreteness-induced fluctuations. For small $N$ (large fluctuations) aperiod-doubling cascade appears as the coupling (migration) increases. As $N$grows an extremely slow dynamic emerges, leading to a flow along aone-dimensional family of almost period 2 solutions. This manifold become atrue solutions in the deterministic limit. The degeneracy between differentattractors that characterizes the clustering phase of the deterministic systemis thus the $N \to \infty$ limit of the slow dynamics manifold.

Globally coupled chaotic maps and demographic stochasticity