Globally coupled chaotic maps and demographic stochasticity
Abstract
The affect of demographic stochasticity of a system of globally coupled chaotic maps is considered. A two-step model is studied, where the intra-patch chaotic dynamics is followed by a migration step that coupled all patches; the equilibrium number of agents on each site, N, controls the strength of the discreteness-induced fluctuations. For small N (large fluctuations) a period-doubling cascade appears as the coupling (migration) increases. As N grows an extremely slow dynamic emerges, leading to a flow along a one-dimensional family of almost period 2 solutions. This manifold become a true solutions in the deterministic limit. The degeneracy between different attractors that characterizes the clustering phase of the deterministic system is thus the N ∞ limit of the slow dynamics manifold.