Randomly connected cellular automata: a search for critical connectivities

I study the Chaté-Manneville cellular-automata rules on randomly connected lattices. The periodic and quasi-periodic macroscopic behaviours associated with these rules on finite-dimensional lattices persist on an infinite-dimensional lattice with finite connectivity and symmetric bonds. The lower critical connectivity for these models is at C=4 and the mean-field connectivity, if finite, is not smaller than C=100. Autocorrelations are found to decay as a power law with a connectivity-independent exponent $\sim -2.5$. A new intermittent chaotic phase is also discussed