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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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    This study introduces prefixed-time synchronization for stochastic networks, improving on fixed-time methods. A novel local intermittent sampling control strategy reduces costs for complex dynamic systems.

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    Area of Science:

    • Control Theory
    • Network Dynamics
    • Stochastic Systems

    Background:

    • Stochastic noise and discontinuous activation are prevalent in real-world engineering systems.
    • Existing fixed-time synchronization methods have limitations in handling these complexities.
    • Dynamic networks with reaction-diffusion terms and delays present significant synchronization challenges.

    Purpose of the Study:

    • To introduce and investigate the novel concept of prefixed-time synchronization.
    • To develop an effective control strategy for stochastic multicoupled delay dynamic networks.
    • To address synchronization issues in systems with discontinuous activation and reaction-diffusion terms.

    Main Methods:

    • Proposal of a local intermittent sampling control strategy in both time and spatial domains.
    • Application of mathematical inequalities (Young's, Jensen's, Hölder's) for analysis.
    • Development of synchronization criteria for networks with and without delays.

    Main Results:

    • Achieved prefixed-time synchronization for stochastic multicoupled delay dynamic networks.
    • Demonstrated reduced control costs through the proposed local intermittent sampling strategy.
    • Established quantitative relationships between control parameters and network scale.

    Conclusions:

    • The proposed prefixed-time synchronization is effective for complex stochastic networks.
    • The local intermittent sampling control strategy offers a practical and cost-efficient solution.
    • The findings are validated by a numerical example using Chua's circuit model.