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    This study addresses the complete stability of delayed neural networks (NNs) across all delay values. A novel frequency-sweeping method offers a systematic solution for analyzing NN stability concerning delays.

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    Area of Science:

    • Control Theory
    • Computational Neuroscience
    • Artificial Intelligence

    Background:

    • Existing research on delayed neural networks (NNs) primarily examines stability intervals starting from zero delay.
    • This limited scope fails to address the complete stability problem across the entire delay axis.

    Purpose of the Study:

    • To investigate the stability properties of delayed neural networks (NNs) comprehensively, considering the entire range of delay parameters.
    • To introduce a novel methodology for solving the complete stability problem in delayed NNs.

    Main Methods:

    • A frequency-sweeping approach is employed to analyze the stability of delayed NNs.
    • The method is designed for general applicability and ease of implementation.

    Main Results:

    • The study demonstrates various types of stability intervals, highlighting the necessity of complete stability analysis.
    • The proposed frequency-sweeping method provides a systematic solution for the complete stability problem with respect to delay.

    Conclusions:

    • The developed frequency-sweeping approach offers a robust and practical solution for analyzing the complete stability of delayed neural networks.
    • This work advances the understanding of stability in NNs with delays, applicable across diverse research areas.