Critical properties of lattices of diffusively coupled quadratic maps

We study the critical properties of lattices of coupled logistic maps in the regime where the individual maps are closely above the onset of chaos. We discuss both spatial and temporal characteristics and especially the link between them. We show that the mutual information function between two points on the lattice decays exponentially with distance. In this way we find support for the relation xi approximately lambda(-1/2) between the coherence length xi and the largest Lyapunov exponent lambda which is further corroborated by a detailed study of the spreading of small perturbations. Finally we study the structure function of the lattice field variable. It shows that at the onset of chaos the lattice remains smooth.