Symmetrizable Boolean networks

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)787-804
Number of pages18
JournalInformation Sciences
StatePublished - May 2023
Externally publishedYes


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


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