  Two-dimensional coupled map lattices have global stability properties that
depend on the coupling between individual maps and their neighborhood. The
action of the neighborhood on individual maps can be implemented in terms of
"causal" coupling (to spatially distant past states) or "non-causal" coupling
(to spatially distant simultaneous states). In this contribution we show that
globally stable behavior of coupled map lattices is facilitated by causal
coupling, thus indicating a surprising relationship between stability and
causality. The influence of causal versus non-causal coupling for synchronous
and asynchronous updating as a function of coupling strength and for different
neighborhoods is analyzed in detail.
