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    This study introduces an event-based, output-quantized control method for achieving global exponential synchronization in multiple time-delay neural networks. It reduces data transmission and ensures system stability without Zeno behavior.

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    Area of Science:

    • Control Theory
    • Computational Neuroscience
    • Network Science

    Background:

    • Synchronization is crucial for collective behavior in complex systems.
    • Neural networks with time delays present unique control challenges.
    • Reducing communication costs is essential for practical control applications.

    Purpose of the Study:

    • To investigate the global exponential synchronization of multiple time-delay neural networks.
    • To develop an event-based output quantized coupling control method.
    • To reduce signal transmission costs and avoid full state observation.

    Main Methods:

    • A dynamic event-triggered mechanism with time-varying control parameters was designed.
    • Output quantized control was employed to minimize data transmission.
    • Halanay-type inequality was utilized to derive synchronization conditions.
    • Zeno behavior was explicitly excluded.

    Main Results:

    • Sufficient conditions for exponential synchronization were established under weakened coupling matrix constraints.
    • The proposed method effectively reduces communication load.
    • The absence of Zeno behavior was demonstrated.
    • Numerical simulations confirmed the theoretical findings.

    Conclusions:

    • The event-based output quantized control strategy ensures global exponential synchronization for multiple time-delay neural networks.
    • The method is efficient in terms of communication and practical for implementation.
    • The theoretical framework is robust and validated by numerical examples.