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arXiv · 0906.0976

Globally coupled chaotic maps and demographic stochasticity

David A. Kessler·Nadav M. Shnerb
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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 $N \to \infty$ limit of the slow dynamics manifold.

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David A. Kessler, Nadav M. Shnerb. 2009-06-04. Globally coupled chaotic maps and demographic stochasticity. https://doi.org/10.1103/physreve.81.036111

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