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Volume 2017 (2017), Article ID 7209762, 6 pages
Research Article

On the Periods of Parallel Dynamical Systems

1Research Institute of Applied Mathematics in Science and Engineering, Ciudad Real, Spain
2Department of Mathematics, University of Castilla-La Mancha, Albacete, Spain

Correspondence should be addressed to Jose C. Valverde

Received 17 June 2016; Revised 20 October 2016; Accepted 16 November 2016; Published 12 January 2017

Academic Editor: David Arroyo

Copyright © 2017 Juan A. Aledo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this work, we provide conditions to obtain fixed point theorems for parallel dynamical systems over graphs with (Boolean) maxterms and minterms as global evolution operators. In order to do that, we previously prove that periodic orbits of different periods cannot coexist, which implies that Sharkovsky’s order is not valid for this kind of dynamical systems.