Periods in XOR parallel dynamical systems over directed dependency graphs

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:364

Article

Kozerenko, Sergiy¹  Valverde, Jose C.² 

[1] Natl Univ Kyiv Mohyla Acad, Dept Math, UA-04070 Kiev, Ukraine

[2] Univ Castilla La Mancha, Dept Math, Albacete 02071, Spain

关键词: Parallel dynamical systems;    Deterministic Boolean networks;    Periodic orbits;    Exclusive disjunction;    Boolean algebra;    Boolean functions;   

DOI  :  10.1016/j.cam.2019.06.029

来源: Elsevier

【 摘 要 】

We analyze the periodic structure of parallel dynamical systems over directed dependency graphs, whose evolution operator is the Boolean function XOR. We prove that such systems can present periodic orbits of any period. Moreover, we demonstrate that any kinds of periods can coexist at the same time. In view of these results, we study the periodic structure of these dynamical systems over complete digraphs, complete bipartite digraphs, acyclic digraphs and out-trees. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free