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Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy.

Jianquan Lu, Jürgen Kurths, Jinde Cao

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    This study introduces a new pinning impulsive control strategy for synchronizing stochastic dynamical networks. The method effectively synchronizes networks using controllers on a small fraction of nodes, ensuring stability and a clear synchronization region.

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    Area of Science:

    • Control Theory
    • Network Synchronization
    • Stochastic Dynamical Systems

    Background:

    • Dynamical networks are crucial in various scientific fields.
    • Synchronization of these networks is essential for coordinated behavior.
    • Existing pinning state feedback controllers are effective but have limitations.

    Purpose of the Study:

    • To propose a novel control strategy for synchronizing stochastic dynamical networks with nonlinear coupling.
    • To demonstrate the effectiveness of pinning impulsive controllers for network synchronization.
    • To establish stability criteria and define the synchronization region for the proposed strategy.

    Main Methods:

    • Development of a new pinning impulsive control strategy.
    • Derivation of generic mean square stability criteria using algebraic conditions.
    • Identification of an effective method for selecting controlled nodes and impulsive constants.
    • Explicitly obtaining the proportion of controlled nodes for stability.

    Main Results:

    • The proposed pinning impulsive control strategy effectively synchronizes stochastic dynamical networks.
    • Mean square stability criteria are derived, guaranteeing synchronization with a small fraction of controlled nodes.
    • An effective node selection method and explicit stability conditions are presented.
    • The synchronization region is clearly defined and visualized.

    Conclusions:

    • Pinning impulsive controllers are effective for synchronizing stochastic dynamical networks.
    • The proposed strategy offers a robust and efficient method for network synchronization.
    • The derived criteria and methods provide practical guidelines for implementing the control strategy.