ISING-TYPE TRANSITIONS IN COUPLED MAP LATTICES

We study, by means of computer simulations, some models of coupled map lattices (CML) with symmetry, subject to diffusive nearest neighbor coupling, with the purpose of providing a better understanding of the occurrence of Ising-type transitions of the type found by Miller and Huse. We argue, on the basis of numerical evidence, that such transitions are connected to the appearance of a minimum in the Lyapunov dimension of the system as a function of the coupling parameter. Two-dimensional CMLs similar to the one in Miller and Huse, but with no minimum in the Lyapunov dimension plot, have no Ising transition. The condition seems to be necessary, though by no means sufficient. We also argue, relying on the analysis of Bunimovich and Sinai, that coupled map lattices should behave differently, with respect to dimension, than Ising models.