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 $N\to \infty$ limit of the slow dynamics manifold.

References in corpus (3)

• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• "Quantum phase transitions" in classical nonequilibrium processes
• Low-dimensional chaos in populations of strongly-coupled noisy maps

Cited by in corpus (2)

• Noise Enhanced Activity in a Complex Network
• Specific behavior of one chaotic dynamics near the fine-structure constant