Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology

Fumito Mori, Atsushi Mochizuki

    Research output: Contribution to journalArticlepeer-review

    11 Citations (Scopus)


    Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.

    Original languageEnglish
    Article number028301
    JournalPhysical review letters
    Issue number2
    Publication statusPublished - Jul 14 2017

    All Science Journal Classification (ASJC) codes

    • Physics and Astronomy(all)


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