American Institute of Mathematical Sciences

Advanced
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 & Continuous Dynamical Systems, 2005, 13 (2) : 491-502. doi: 10.3934/dcds.2005.13.491
[1]

T.K. Subrahmonian Moothathu. Homogeneity of surjective cellular automata. Discrete & Continuous Dynamical Systems, 2005, 13 (1) : 195-202. doi: 10.3934/dcds.2005.13.195
[2]

Achilles Beros, Monique Chyba, Oleksandr Markovichenko. Controlled cellular automata. Networks & Heterogeneous Media, 2019, 14 (1) : 1-22. doi: 10.3934/nhm.2019001
[3]

Marcus Pivato. Invariant measures for bipermutative cellular automata. Discrete & Continuous Dynamical Systems, 2005, 12 (4) : 723-736. doi: 10.3934/dcds.2005.12.723
[4]

Achilles Beros, Monique Chyba, Kari Noe. Co-evolving cellular automata for morphogenesis. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2053-2071. doi: 10.3934/dcdsb.2019084
[5]

Micol Amar. A note on boundary layer effects in periodic homogenization with Dirichlet boundary conditions. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 537-556. doi: 10.3934/dcds.2000.6.537
[6]

Bernard Host, Alejandro Maass, Servet Martínez. Uniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules. Discrete & Continuous Dynamical Systems, 2003, 9 (6) : 1423-1446. doi: 10.3934/dcds.2003.9.1423
[7]

Marcelo Sobottka. Right-permutative cellular automata on topological Markov chains. Discrete & Continuous Dynamical Systems, 2008, 20 (4) : 1095-1109. doi: 10.3934/dcds.2008.20.1095
[8]

Xinxin Tan, Shujuan Li, Sisi Liu, Zhiwei Zhao, Lisa Huang, Jiatai Gang. Dynamic simulation of a SEIQR-V epidemic model based on cellular automata. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 327-337. doi: 10.3934/naco.2015.5.327
[9]

Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209
[10]

Carmen Calvo-Jurado, Juan Casado-Díaz, Manuel Luna-Laynez. Parabolic problems with varying operators and Dirichlet and Neumann boundary conditions on varying sets. Conference Publications, 2007, 2007 (Special) : 181-190. doi: 10.3934/proc.2007.2007.181
[11]

Tian Ma, Shouhong Wang. Structure of 2D incompressible flows with the Dirichlet boundary conditions. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 29-41. doi: 10.3934/dcdsb.2001.1.29
[12]

Nicola Abatangelo, Serena Dipierro, Mouhamed Moustapha Fall, Sven Jarohs, Alberto Saldaña. Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions. Discrete & Continuous Dynamical Systems, 2019, 39 (3) : 1205-1235. doi: 10.3934/dcds.2019052
[13]

Le Thi Phuong Ngoc, Khong Thi Thao Uyen, Nguyen Huu Nhan, Nguyen Thanh Long. On a system of nonlinear pseudoparabolic equations with Robin-Dirichlet boundary conditions. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021190
[14]

Leslaw Skrzypek, Yuncheng You. Feedback synchronization of FHN cellular neural networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (12) : 6047-6056. doi: 10.3934/dcdsb.2021001
[15]

Long Hu, Tatsien Li, Bopeng Rao. Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type. Communications on Pure & Applied Analysis, 2014, 13 (2) : 881-901. doi: 10.3934/cpaa.2014.13.881
[16]

Lin Wang, James Watmough, Fang Yu. Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions. Mathematical Biosciences & Engineering, 2015, 12 (4) : 699-715. doi: 10.3934/mbe.2015.12.699
[17]

E. C.M. Crooks, E. N. Dancer, Danielle Hilhorst. Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 39-44. doi: 10.3934/dcdsb.2007.8.39
[18]

Sándor Kelemen, Pavol Quittner. Boundedness and a priori estimates of solutions to elliptic systems with Dirichlet-Neumann boundary conditions. Communications on Pure & Applied Analysis, 2010, 9 (3) : 731-740. doi: 10.3934/cpaa.2010.9.731
[19]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2357-2376. doi: 10.3934/cpaa.2017116
[20]

Marek Fila, Hirokazu Ninomiya, Juan-Luis Vázquez. Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems. Discrete & Continuous Dynamical Systems, 2006, 14 (1) : 63-74. doi: 10.3934/dcds.2006.14.63

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (35)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy