Master--slave synchronization of affine cellular automaton pairs

Gelasio Salaza; Edgardo Ugalde; Jesús Urías

doi:10.3934/dcds.2005.13.491

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2005, Volume 13, Issue 2: 491-502. Doi: 10.3934/dcds.2005.13.491

This issue Previous Article Lyapunov exponents for continuous transformations and dimension theory Next Article Rate of convergence for correctors in almost periodic homogenization

Master--slave synchronization of affine cellular automaton pairs

1.
Instituto de Física, UASLP, Alvaro Obregon 64, San Luis Potosí, SLP, 78000 México

Received: September 30, 2004

Revised: March 31, 2005

Published: January 2005

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Abstract

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.

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Mathematics Subject Classification: 15A33, 37B15, 15A90.

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