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Stability and Stabilization in Probability of Probabilistic Boolean Networks.

Chi Huang, Jianquan Lu, Guisheng Zhai

    IEEE Transactions on Neural Networks and Learning Systems
    |March 29, 2020
    PubMed
    Summary
    This summary is machine-generated.

    This study explores probabilistic Boolean networks and control networks, extending stability analysis beyond strict probability one. New conditions ensure system stabilization even with indefinite target state probabilities.

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    Area of Science:

    • Systems Biology
    • Control Theory
    • Network Science

    Background:

    • Probabilistic Boolean networks (PBNs) model complex biological systems.
    • Traditional stability analysis requires strict probability one, limiting realistic simulations.
    • Cellular systems often exhibit indefinite state transitions.

    Purpose of the Study:

    • To investigate probability stability in PBNs and probabilistic Boolean control networks.
    • To extend stability analysis to non-strict probability conditions for realistic cellular modeling.
    • To develop methods for systems where target states have indefinite self-transfer probabilities.

    Main Methods:

    • Utilizing the semitensor product of matrices for analysis.
    • Developing necessary and sufficient conditions for stability and stabilization.
    • Extending traditional probability-one stability problems.

    Main Results:

    • Established conditions for probability stability in PBNs.
    • Provided criteria for stabilization in probabilistic Boolean control networks under relaxed probability constraints.
    • Demonstrated the effectiveness of the semitensor product approach.

    Conclusions:

    • The semitensor product method offers a robust framework for analyzing PBNs with non-strict stability.
    • The findings advance the modeling and control of complex biological systems.
    • This work provides a valuable extension to existing network stability theories.