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Partial Synchronization of Interconnected Boolean Networks.

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    Summary
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    This study presents criteria for partial synchronization in interconnected Boolean networks (BNs) using the semi-tensor product (STP) method. It offers a graphical approach for analyzing BN synchronization, validated with an epigenetic model example.

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    Area of Science:

    • Control Theory
    • Network Science
    • Computational Biology

    Background:

    • Boolean networks (BNs) are widely used to model complex biological systems.
    • Understanding synchronization in interconnected BNs is crucial for predicting system behavior.

    Purpose of the Study:

    • To develop criteria for achieving partial synchronization in interconnected Boolean networks.
    • To establish a graphical method for analyzing partial synchronization.

    Main Methods:

    • Utilizing the semi-tensor product (STP) of matrices for algebraic state space representation of BNs.
    • Defining an induced digraph based on the set of partially synchronized states.
    • Deriving synchronization criteria using the adjacency matrix of the induced digraph.

    Main Results:

    • A necessary and sufficient criterion for partial synchronization of interconnected BNs was established.
    • An equivalent graphical description for partial synchronization was developed.
    • A second criterion for partial synchronization was derived using graph theory.

    Conclusions:

    • The proposed methods provide efficient criteria for analyzing partial synchronization in Boolean networks.
    • The graphical approach offers intuitive insights into network synchronization dynamics.
    • The findings are validated through examples, including a relevant epigenetic model.