Journal of Applied Mathematics

Parallel Dynamical Systems over Graphs and Related Topics: A Survey

Juan A. Aledo, Silvia Martinez, and Jose C. Valverde

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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.

Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 594294, 14 pages.

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1429105054

Digital Object Identifier
doi:10.1155/2015/594294

Mathematical Reviews number (MathSciNet)
MR3332130

Citation

Aledo, Juan A.; Martinez, Silvia; Valverde, Jose C. Parallel Dynamical Systems over Graphs and Related Topics: A Survey. J. Appl. Math. 2015 (2015), Article ID 594294, 14 pages. doi:10.1155/2015/594294. https://projecteuclid.org/euclid.jam/1429105054


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