Migration in cellular automata

✍ Scribed by Birgitt Schönfisch; Claude Lacoursière

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 963 KB
• Volume: 103
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(96)00284-9

✦ Synopsis

We investigate the effect of spatial migration of cells in cellular automata that have been used in the study of excitable media and epidemiology, with an infinite range migration. While the periods of oscillation of the densities of cells in each state are mostly unaffected by migration, the amplitudes of these oscillations behave very differently when migration is present. Spatial structures which develop in the absence of migration are shown to be unstable to even the lowest possible level of migration. Decay of these structures is shown to scale with system size, demonstrating the absence of structure in the asymptotic regime fi~r any system size. Decay of structure is also shown to occur on a time scale, T, scaling roughly as T ~ t • m, where m is the migration rate and t is time elapsed. The exact shape of the decay of structure, however, is not self-similar, Overall, structure decays almost entirely after each cell has migrated twice on an average. We conclude from this that the asymptotic behavior, after the structure has subsided, is governed by the mean field approximation.