Predecessors and Gardens of Eden in sequential dynamical systems over directed graphs-Reference-Cited by-同舟云学术

Predecessors and Gardens of Eden in sequential dynamical systems over directed graphs

Published:2018-07-01 Issue:2 Volume:3 Page:593-602
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Aledo Juan A.¹,Diaz Luis G.¹,Martinez Silvia²,Valverde Jose C.²

Affiliation:

1. Institute of Applied Mathematics in Science and Engineering , Ciudad Real , Spain

2. Department of Mathematics University of Castilla - La Mancha , Albacete , Spain

Abstract

Abstract In this work, we deal with the predecessors existence problems in sequential dynamical systems over directed graphs. The results given in this paper extend those existing for such systems over undirected graphs. In particular, we solve the problems on the existence, uniqueness and coexistence of predecessors of any given state vector, characterizing the Garden-of-Eden states at the same time. We are also able to provide a bound for the number of predecessors and Garden-of-Eden state vectors of any of these systems.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.2478/AMNS.2018.2.00046

Reference28 articles.

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3. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, On periods and equilibria of sequential dynamical systems, Inf. Sci. 409–410 (2017) 27–34. 10.1016/j.ins.2017.05.002.

4. J.A. Aledo, L.G. Diaz, S. Martinez and J.C. Valverde, Maximum number of periodic orbits in parallel dynamical systems, Inf. Sci. 468 (2018) 63–71. 10.1016/j.ins.2018.08.041.

5. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, Predecessors and Garden-of-Eden configurations in parallel dynamical models, J. Comput. Appl. Math. 348 (2019) 26–33. 10.1016/j.cam.2018.08.015.

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