2ND-ORDER DYNAMICS IN THE COLLECTIVE TEMPORAL EVOLUTION OF COMPLEX-SYSTEMS

Dynamics involving a discrete second-order time derivative captures many essential, previously unexplained features of the collective behavior of complex, spatially extended systems such as cellular automata and coupled-map lattices. We argue that irrational frequencies can emerge from discrete-time dynamics, and that the second-order dynamics makes previous droplet-type arguments irrelevant for these models. These findings are supported by numerical examples.