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    Area of Science:

    • Systems Biology
    • Control Theory
    • Network Science

    Background:

    • Temporal Boolean networks (TBNs) are crucial for modeling complex biological systems.
    • Data loss in information transmission can significantly impact the stability and behavior of TBNs.
    • Understanding long-run behavior and asymptotic stability is essential for reliable TBN applications.

    Purpose of the Study:

    • To investigate the asymptotic stability of TBNs with multiple data losses.
    • To develop methods for analyzing and ensuring synchronization between ideal TBNs and those with data loss.
    • To provide a theoretical framework for TBNs operating under noisy conditions.

    Main Methods:

    • Modeling information transmission using Bernoulli variables.
    • Constructing an augmented system to analyze the original TBN.
    • Deriving an auxiliary system to study synchronization issues.
    • Developing necessary and sufficient conditions for asymptotic stability.

    Main Results:

    • A theorem establishing the equivalence between the stability of the original and augmented systems.
    • A necessary and sufficient condition for determining the asymptotic stability of TBNs with data loss.
    • An effective criterion for verifying synchronization between ideal and data-losing TBNs.

    Conclusions:

    • The proposed methods effectively analyze the long-run behavior and stability of TBNs with data loss.
    • The findings provide a robust framework for designing and controlling TBNs in the presence of transmission errors.
    • Numerical examples validate the theoretical results, demonstrating practical applicability.