TY - JOUR
T1 - Symmetrizable Boolean networks
AU - Aledo, Juan A.
AU - Goles, Eric
AU - Montalva-Medel, Marco
AU - Montealegre, Pedro
AU - Valverde, Jose C.
N1 - Funding Information:
Juan A. Aledo has been funded by the Government of Castilla-La Mancha and “ERDF A way of making Europe” through the project SBPLY/17/180501/000493. It is also part of the project PID2019-106758 GB-C33 funded by MCIN/AEI. Jose C. Valverde was supported by the FEDER OP2014-2020 and the University of Castilla-La Mancha under Grant 2021-GRIN-31241, by the Junta de Comunidades de Castilla-La Mancha under grant SBPLY/21/180501/000174, and by the Ministry of Economy and Competitiveness of Spain under the Grant PGC2018-097198-B-I00. Eric Goles and Pedro Montealegre have been partially funded by the Chilean FONDECYT-ANID project 1200006, by Centro de Modelamiento Matemático (CMM), FB210005, BASAL funds for centers of excellence from ANID-Chile and, together with Marco Montalva, by Programa Regional STIC-AmSud (CoDANet) céd. 19 STIC-03. Pedro Montealegre also acknowledges the financial support of FONDECYT-ANID project 11190482.
Publisher Copyright:
© 2023 The Author(s)
PY - 2023/5
Y1 - 2023/5
N2 - In this work, we provide a procedure that allows us to transform certain kinds of deterministic Boolean networks on minterm or maxterm functions into symmetric ones, so inferring that such symmetrizable networks can present only periodic points of periods 1 or 2. In particular, we deal with generalized parallel (or synchronous) dynamical systems (GPDS) over undirected graphs, i.e., discrete parallel dynamical systems over undirected graphs where some of the self-loops may not appear. We also study the class of anti-symmetric GPDS (which are non-symmetrizable), proving that their periodic orbits have period 4. In addition, we introduce a class of non-symmetrizable systems which admit periodic orbits with arbitrary large periods.
AB - In this work, we provide a procedure that allows us to transform certain kinds of deterministic Boolean networks on minterm or maxterm functions into symmetric ones, so inferring that such symmetrizable networks can present only periodic points of periods 1 or 2. In particular, we deal with generalized parallel (or synchronous) dynamical systems (GPDS) over undirected graphs, i.e., discrete parallel dynamical systems over undirected graphs where some of the self-loops may not appear. We also study the class of anti-symmetric GPDS (which are non-symmetrizable), proving that their periodic orbits have period 4. In addition, we introduce a class of non-symmetrizable systems which admit periodic orbits with arbitrary large periods.
KW - Generalized parallel dynamical system
KW - Limit cycles
KW - Period structure
KW - Symmetric and anti-symmetric networks
KW - Symmetrizable networks
UR - http://www.scopus.com/inward/record.url?scp=85146554689&partnerID=8YFLogxK
U2 - 10.1016/j.ins.2023.01.082
DO - 10.1016/j.ins.2023.01.082
M3 - Article
AN - SCOPUS:85146554689
SN - 0020-0255
VL - 626
SP - 787
EP - 804
JO - Information Sciences
JF - Information Sciences
ER -