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Parallel Dynamical Systems over Graphs and Related Topics: A Survey

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  • Juan A. Aledo
  • Silvia Martinez
  • Jose C. Valverde

Abstract

In discrete processes, as computational or genetic ones, there are many entities and each entity has a state at a given time. The update of states of the entities constitutes an evolution in time of the system, that is, a discrete dynamical system. The relations among entities are usually represented by a graph. The update of the states is determined by the relations of the entities and some local functions which together constitute (global) evolution operator of the dynamical system. If the states of the entities are updated in a synchronous manner, the system is called a parallel dynamical system . This paper is devoted to review the main results on the dynamical behavior of parallel dynamical systems over graphs which constitute a generic tool for modeling discrete processes.

Suggested Citation

  • Juan A. Aledo & Silvia Martinez & Jose C. Valverde, 2015. "Parallel Dynamical Systems over Graphs and Related Topics: A Survey," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-14, March.
    • Handle: RePEc:hin:jnljam:594294
    DOI: 10.1155/2015/594294
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    Cited by:

    1. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Dynamical attraction in parallel network models," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 874-888.
    2. Sara D. Cardell & Amparo Fúster-Sabater, 2019. "Binomial Representation of Cryptographic Binary Sequences and Its Relation to Cellular Automata," Complexity, Hindawi, vol. 2019, pages 1-13, March.
    3. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2017. "On the Periods of Parallel Dynamical Systems," Complexity, Hindawi, vol. 2017, pages 1-6, January.
    4. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2019. "Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems," Complexity, Hindawi, vol. 2019, pages 1-10, March.
    5. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Solution to the predecessors and Gardens-of-Eden problems for synchronous systems over directed graphs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 22-28.
    6. Mauro Mezzini & Fernando L. Pelayo, 2020. "An Algorithm for Counting the Fixed Point Orbits of an AND-OR Dynamical System with Symmetric Positive Dependency Graph," Mathematics, MDPI, vol. 8(9), pages 1-9, September.

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