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    Area of Science:

    • Control Systems
    • Computational Neuroscience
    • Applied Mathematics

    Background:

    • Discontinuous neural networks with delays present synchronization challenges.
    • Achieving finite-/fixed-time synchronization is crucial for reliable network performance.
    • Existing methods may lack precision in estimating convergence times.

    Purpose of the Study:

    • To develop a unified framework for finite-/fixed-time synchronization of delayed coupled discontinuous neural networks.
    • To design novel controllers ensuring precise synchronization and accurate setting time estimations.
    • To provide criteria for selecting controller parameters for guaranteed convergence.

    Main Methods:

    • Utilizing a unified framework for analyzing synchronization.
    • Designing two novel controllers, including a switching controller.
    • Applying finite-/fixed-time theorems and Lyapunov function theory.
    • Deriving criteria for controller parameter selection.

    Main Results:

    • Novel control protocols were established for finite-/fixed-time synchronization.
    • Criteria for controller parameter selection were derived.
    • The proposed methods guarantee error system convergence within finite/fixed time.
    • Accurate estimations for setting times were provided.

    Conclusions:

    • The proposed control protocols effectively achieve finite-/fixed-time synchronization for delayed discontinuous neural networks.
    • The developed criteria ensure reliable controller parameter selection.
    • Numerical examples validate the efficiency of the proposed synchronization strategies.