Randomly connected cellular automata: a search for critical connectivities
Theoretical Physics, University of Oxford - 1 Keble Road, Oxford OX1
Accepted: 18 January 1996
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 . A new intermittent chaotic phase is also discussed.
PACS: 05.50.+q – Lattice theory and statistics; Ising problems / 05.45.+b – Theory and models of chaotic systems / 03.20.+i – Classical mechanics of discrete systems: general mathematical aspects
© EDP Sciences, 1996