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    This study introduces a new continuous control method for fixed-time synchronization (FDTS) in complex networks with stochastic perturbations, avoiding chattering. The developed criteria are broadly applicable to various network types.

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    Area of Science:

    • Complex Networks
    • Control Theory
    • Stochastic Systems

    Background:

    • Complex networks are fundamental to many systems, but achieving synchronization under stochastic perturbations remains challenging.
    • Previous synchronization methods often suffer from the chattering phenomenon due to discontinuous controllers.

    Purpose of the Study:

    • To investigate and achieve fixed-time synchronization (FDTS) in complex networks subject to stochastic perturbations.
    • To develop a novel, continuous control scheme that avoids the chattering phenomenon.

    Main Methods:

    • Design of a new continuous controller without a sign function.
    • Utilization of Lyapunov functionals and properties of the Weiner process.
    • Application of a designed comparison system to derive synchronization criteria.

    Main Results:

    • Several criteria for achieving FDTS in complex networks with stochastic perturbations are established.
    • The proposed control scheme is continuous, effectively mitigating the chattering issue.
    • The derived synchronization criteria are general, applicable to both directed and undirected weighted networks.

    Conclusions:

    • The study successfully demonstrates a robust method for fixed-time synchronization in complex stochastic networks.
    • The developed continuous control strategy offers an improvement over existing methods by eliminating chattering.
    • The broad applicability of the synchronization criteria highlights the practical potential of the findings.