  The early-time critical dynamics of continuous, Ising-like phase transitions
is studied numerically for two-dimensional lattices of coupled chaotic maps.
Emphasis is laid on obtaining accurate estimates of the dynamic critical
exponents \theta' 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.
