Symmetrizable Boolean networks

Juan A. Aledo; Eric Goles; Marco Montalva-Medel; Pedro Montealegre; Jose C. Valverde

doi:10.1016/j.ins.2023.01.082

Symmetrizable Boolean networks

Juan A. Aledo, Eric Goles, Marco Montalva-Medel, Pedro Montealegre, Jose C. Valverde

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	787-804
Number of pages	18
Journal	Information Sciences
Volume	626
DOIs	https://doi.org/10.1016/j.ins.2023.01.082
State	Published - May 2023
Externally published	Yes

Keywords

Generalized parallel dynamical system
Limit cycles
Period structure
Symmetric and anti-symmetric networks
Symmetrizable networks

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10.1016/j.ins.2023.01.082

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abstract = "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.",

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T1 - Symmetrizable Boolean networks

AU - Aledo, Juan A.

AU - Goles, Eric

AU - Montalva-Medel, Marco

AU - Montealegre, Pedro

AU - Valverde, Jose C.

PY - 2023/5

Y1 - 2023/5

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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

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SP - 787

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Symmetrizable Boolean networks

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Keywords

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