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    Area of Science:

    • Complex Systems and Networks
    • Nonlinear Dynamics
    • Control Theory

    Background:

    • Reaction-diffusion neural networks (RDNNs) are crucial for modeling spatio-temporal phenomena.
    • Synchronization of coupled RDNNs is essential for understanding complex system behaviors.
    • Parameter uncertainties and spatial diffusion introduce significant challenges in achieving robust synchronization.

    Purpose of the Study:

    • To investigate the robust H∞ synchronization of two types of coupled RDNNs.
    • To develop pinning adaptive control strategies for achieving H∞ synchronization.
    • To address synchronization challenges posed by multiple state/spatial couplings and parameter uncertainties.

    Main Methods:

    • Lyapunov functional combined with inequality techniques to derive synchronization conditions.
    • Design of node-based pinning adaptive controllers for robust H∞ synchronization.
    • Development of edge-based pinning adaptive controllers for synchronization under parameter uncertainties.

    Main Results:

    • Sufficient conditions for robust H∞ synchronization of coupled RDNNs with parameter uncertainties were established.
    • Node-based and edge-based pinning adaptive control strategies effectively achieve H∞ synchronization.
    • Numerical examples validated the theoretical findings and the efficacy of the proposed control methods.

    Conclusions:

    • The proposed pinning adaptive control strategies guarantee robust H∞ synchronization for the considered coupled RDNNs.
    • The developed criteria provide effective means to ensure synchronization performance despite parameter variations and complex couplings.
    • This work contributes to the theoretical understanding and practical control of complex neural network systems.