From: Hugues Chat'e (chate@amoco.saclay.cea.fr)
Date: Fri Mar 26 1993 - 13:29:34 UTC
Here follows a list of our papers on "collective behavior", in CA and in coupled map lattices, where similar phenomenology was found. Briefly, using CA as example, the behavior are best described as a small-dynamical-system-like macroscopic evolution (e.g. the density of one type of sites follows a periodic cycle with a period commensurate or not with the updating "clock"), arising from a spatially-homogeneous local disorder (similar to class 3 CAs). Actually, one can see these models as class 3 CA in which the density is not a fixed point in the infinite-size limit, but, again, follows some low-dimensional dynamics. There exists a "thermodynamic limit": the fluctuations around the macroscopic behavior are roughly Gaussian, and decrease like N^(-1/2) where N is the number of sites in the lattice. Extensive search for rules, and numerous tests of the robustness of the behavior was realized; as of this date, there is no available theory; several people are currently working on this problem: H. Herrmann (et al), J. Gallas, P Grassberger, Y. Pomeau, Y Kuramoto. We have also to mention V Privman and Ph Binder, although their claims about "explaining" things are, I believe, abusive. There is one (long, comprehensive) paper: H. Chate and P. Manneville, Progress of Theoretical Physics, vol.87, pp1-60, (1992). which was accompanied by a few letters: H. Chate and P Manneville, Europhysics Letters 14 (1991) 409. H. Chate and P Manneville, Europhysics Letters 17 (1992) 291. B. Barral, H. Chate and P Manneville, Physics Letters A 163 (1992) 279. Reprints are available on request....
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