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    Area of Science:

    • Systems Biology
    • Control Theory
    • Computational Neuroscience

    Background:

    • Dynamic-algebraic Boolean networks (DABNs) are crucial for modeling complex biological systems.
    • Understanding the solvability and uniqueness of DABN solutions is essential for accurate predictions.
    • Existing methods for DABN analysis can be computationally intensive.

    Purpose of the Study:

    • To develop a novel normalization technique for DABNs.
    • To establish necessary and sufficient conditions for the solvability and uniqueness of DABN solutions.
    • To investigate the application of pinning control for ensuring DABN solution properties.

    Main Methods:

    • Derivation of a new expression for normalized DABNs.
    • Analytical investigation of solvability and uniqueness conditions.
    • Application of pinning control strategies.

    Main Results:

    • A new normalization expression for DABNs was successfully obtained.
    • Necessary and sufficient conditions for DABN solvability and uniqueness were established.
    • The effectiveness of pinning control in ensuring solution properties was demonstrated.

    Conclusions:

    • The proposed normalization method provides a foundation for analyzing DABNs.
    • The derived conditions offer precise criteria for assessing DABN solutions.
    • Pinning control is a viable strategy for enhancing DABN analysis and control.