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Synchronization for the Realization-Dependent Probabilistic Boolean Networks.

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    This study presents a method for synchronizing probabilistic Boolean networks (PBNs) in a drive-response setup. It provides a computable algebraic criterion to ensure PBN synchronization, demonstrated with examples.

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    Area of Science:

    • Control Theory
    • Network Science
    • Computational Biology

    Background:

    • Probabilistic Boolean networks (PBNs) are widely used to model complex biological systems.
    • Synchronization is a key phenomenon in coupled dynamical systems, including PBNs.
    • Understanding synchronization in PBNs is crucial for predicting and controlling system behavior.

    Purpose of the Study:

    • To investigate and establish conditions for the synchronization of unidirectionally coupled drive-response probabilistic Boolean networks (PBNs).
    • To develop an easily computable algebraic criterion for ensuring PBN synchronization.
    • To demonstrate the practical applicability of the proposed synchronization method.

    Main Methods:

    • Algebraic representation of drive-response PBNs using the semitensor product method.
    • Development of a novel matrix operator to define the reachable set of states.
    • Derivation of a necessary and sufficient condition for PBN synchronization.

    Main Results:

    • A precise algebraic condition for the synchronization of realization-dependent PBNs is established.
    • A new matrix operator facilitates the representation of reachable states as a column vector.
    • An easily computable algebraic criterion is derived for assuring synchronization.

    Conclusions:

    • The proposed method provides a robust framework for analyzing and achieving synchronization in PBNs.
    • The developed algebraic criterion is efficient and applicable to various PBN configurations.
    • The findings offer valuable insights for the control and design of complex biological networks.