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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, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnljam:v:2015:y:2015:i:1:n:594294
    DOI: 10.1155/2015/594294
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    References listed on IDEAS

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    1. Chiaselotti, G. & Gentile, T. & Oliverio, P.A., 2014. "Parallel and sequential dynamics of two discrete models of signed integer partitions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1249-1261.
    2. Ricard V. Solé & Bartolo Luque & Stuart Kauffman, 2000. "Phase Transitions in Random Networks with Multiple States," Working Papers 00-02-011, Santa Fe Institute.
    3. G. Chiaselotti & G. Marino & P. A. Oliverio & D. Petrassi, 2013. "A Discrete Dynamical Model of Signed Partitions," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, April.
    4. G. Chiaselotti & T. Gentile & G. Marino & P. A. Oliverio, 2013. "Parallel Rank of Two Sandpile Models of Signed Integer Partitions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Rickert, M. & Nagel, K. & Schreckenberg, M. & Latour, A., 1996. "Two lane traffic simulations using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(4), pages 534-550.
    6. G. Chiaselotti & T. Gentile & G. Marino & P. A. Oliverio, 2013. "Parallel Rank of Two Sandpile Models of Signed Integer Partitions," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-12, April.
    7. G. Chiaselotti & G. Marino & P. A. Oliverio & D. Petrassi, 2013. "A Discrete Dynamical Model of Signed Partitions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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