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February  2005, 13(2): 491-502. doi: 10.3934/dcds.2005.13.491

Master--slave synchronization of affine cellular automaton pairs

Gelasio Salaza 1, , Edgardo Ugalde 1, and  Jesús Urías 1,

1. 

Instituto de Física, UASLP, Alvaro Obregon 64, San Luis Potosí, SLP, 78000 México, Mexico

Received  October 2004 Revised  April 2005 Published  April 2005

Necessary and sufficient conditions are given for master--slave synchronization of any pair of unidirectionally coupled one--dimensional affine cellular automata of rank one. In each case the synchronization condition is expressed in terms of the coupling and the arithmetic properties of the automaton local rule. The asymptotic behavior of finite length affine automata of rank one, subjected to Dirichlet boundary conditions, is shown to be equivalent to the synchronization problem.
Keywords: nilpotency., Dirichlet boundary conditions, synchronization, Cellular automata.
Mathematics Subject Classification: 15A33, 37B15, 15A9.
Citation: Gelasio Salaza, Edgardo Ugalde, Jesús Urías. Master--slave synchronization of affine cellular automaton pairs. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 491-502. doi: 10.3934/dcds.2005.13.491
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