Randomly connected cellular automata: A search for critical connectivities
arXiv:cond-mat/9603130 · doi:10.1209/epl/i1996-00370-1
Abstract
I study the Chate-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 approx. equal to -2.5. A new intermitten chaotic phase is also discussed.
9 pages, 5 figures, compressed with uufiles. One figure (too large) missing, available via e-mail ([email protected]) To appear in Europhys. Lett