Early-time critical dynamics of lattices of coupled chaotic maps

Abstract

The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is placed on obtaining accurate estimates of the dynamic critical exponents ${\ensuremath{\theta}}^{\ensuremath{'}}$ and $z$. The critical points of five different models are investigated, varying the mode of update, the coupling, and the local map. Our results suggest that the nature of update is a relevant parameter for dynamic universality classes of extended dynamical systems, generalizing results obtained previously for the static properties. They also indicate that the universality observed for the static properties of Ising-like transitions of synchronously updated systems does not hold for their dynamic critical properties.