Emergence of patterns in driven and in autonomous spatiotemporal systems.

The relationship between driven and autonomous spatiotemporal systems is
investigated in the context of coupled map lattice models. Specifically, a
locally coupled map lattice subjected to an external drive is compared to
a coupled map system with similar local couplings plus a global
interaction. It is shown that, under some conditions, the emergent
patterns and the phenomenon of synchronization are analogous in both
systems. Based on the knowledge of the dynamical responses of the driven
lattice, we present a method that allows the prediction of parameter
values for the emergence of ordered spatiotemporal patterns in classes of
coupled map systems having the same local couplings and general forms of
global interactions. It is also shown that synchronized states in both
kinds of systems are equivalent, but the collective states arising after
the chaotic synchronized state becomes unstable can be different in each
case. It is found that an external drive induces chaotic synchronization
as well as synchronization of unstable periodic orbits of the local
dynamics in the driven lattice. On the other hand, the addition of a
global interaction in the autonomous system allows for chaotic
synchronization which is not possible in large coupled map systems
possessing only local couplings.