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    This study achieves global exponential synchronization for multiple neural networks (NNs) with time delays using an event-triggered coupling strategy. The derived conditions ensure synchronization regardless of the coupling matrix type or subsystem effects.

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    Area of Science:

    • Complex Systems
    • Control Theory
    • Computational Neuroscience

    Background:

    • Neural networks (NNs) are crucial for complex system modeling.
    • Synchronization in NNs is vital for emergent behaviors.
    • Time delays and event-triggered control present significant challenges.

    Purpose of the Study:

    • To investigate global exponential synchronization of multiple NNs with time delays.
    • To develop an event-triggered coupling strategy for synchronization.
    • To analyze the impact of non-Laplacian coupling matrices and subsystem effects.

    Main Methods:

    • Utilizing an event-triggered control strategy for coupling.
    • Deriving sufficient conditions for global exponential synchronization.
    • Employing theoretical analysis for coupled NNs with time delays.

    Main Results:

    • Established a broad class of event-triggered coupling for NN synchronization.
    • Developed simple and convenient sufficient conditions for guaranteed synchronization.
    • Demonstrated that subsystem effects can be positive or negative.

    Conclusions:

    • The proposed event-triggered strategy effectively achieves global exponential synchronization.
    • The derived conditions are applicable to a wide range of coupling scenarios.
    • The findings offer practical insights into designing synchronized NN systems.