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Synchronization in Coupled Neural Networks With Hybrid Delayed Impulses: Average Impulsive Delay-Gain Method.

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    Summary
    This summary is machine-generated.

    We introduce average impulsive delay-gain (AIDG) to analyze coupled neural networks (CNNs) synchronization. Our novel criteria offer flexible solutions for complex systems, proving AIDG impacts synchronization positively and negatively.

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    Area of Science:

    • Neuroscience
    • Control Theory
    • Network Science

    Background:

    • Coupled Neural Networks (CNNs) are fundamental to understanding complex brain functions.
    • Synchronization in CNNs is crucial for information processing but challenging due to delayed impulses.
    • Existing methods often lack flexibility in handling time-varying parameters.

    Purpose of the Study:

    • To introduce a new metric, average impulsive delay-gain (AIDG), for analyzing CNN synchronization.
    • To develop novel, less conservative synchronization criteria for CNNs with hybrid delayed impulses.
    • To investigate the dual (positive and negative) effects of AIDG on network synchronization.

    Main Methods:

    • Development of novel globally exponential synchronization criteria.
    • Analysis based on impulsive control and impulsive perturbation theory.
    • Application of the Average Impulsive Delay-Gain (AIDG) concept.

    Main Results:

    • Established new synchronization criteria applicable to hybrid delayed impulses with time-varying delays and gains.
    • Demonstrated that AIDG can both facilitate and hinder synchronization.
    • Showcased the flexibility and reduced conservatism of the proposed methods.

    Conclusions:

    • The AIDG concept provides a more comprehensive framework for CNN synchronization analysis.
    • The derived criteria are more broadly applicable than existing methods.
    • The findings were validated on small-world and scale-free network models.