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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<jats:italic>parallel dynamical system<\/jats:italic>. 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.<\/jats:p>","DOI":"10.1155\/2015\/594294","type":"journal-article","created":{"date-parts":[[2015,3,24]],"date-time":"2015-03-24T19:32:18Z","timestamp":1427225538000},"page":"1-14","source":"Crossref","is-referenced-by-count":21,"title":["Parallel Dynamical Systems over Graphs and Related Topics: A Survey"],"prefix":"10.1155","volume":"2015","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1786-8087","authenticated-orcid":true,"given":"Juan A.","family":"Aledo","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Silvia","family":"Martinez","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, 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