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Dynamics of Random Boolean Networks under Fully Asynchronous Stochastic Update Based on Linear Representation

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  • Chao Luo
  • Xingyuan Wang

Abstract

A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.

Suggested Citation

  • Chao Luo & Xingyuan Wang, 2013. "Dynamics of Random Boolean Networks under Fully Asynchronous Stochastic Update Based on Linear Representation," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-12, June.
    • Handle: RePEc:plo:pone00:0066491
    DOI: 10.1371/journal.pone.0066491
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    Cited by:

    1. Xiangshan Kong & Qilong Sun & Haitao Li, 2022. "Survey on Mathematical Models and Methods of Complex Logical Dynamical Systems," Mathematics, MDPI, vol. 10(20), pages 1-17, October.

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