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    This study achieves synchronization in complex dynamical networks with semi-Markov switching topology using a novel dynamic-memory event-triggered protocol. This method enhances control and reduces data transmission for stochastic systems.

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    Area of Science:

    • Complex dynamical networks
    • Stochastic systems
    • Control theory

    Background:

    • Reaction-diffusion complex dynamical networks (CDNs) exhibit complex behaviors.
    • Semi-Markov processes introduce stochasticity into network topology switching.
    • Event-triggered control strategies aim to reduce communication load.

    Purpose of the Study:

    • Investigate synchronization in stochastic jump CDNs with semi-Markov switching topology.
    • Develop a dynamic-memory event-triggered protocol for enhanced control.
    • Reduce data transmission while ensuring synchronization.

    Main Methods:

    • Utilized a semi-Markov process to model stochastic topology switching.
    • Proposed a dynamic-memory event-triggered strategy based on internal dynamic variable history.
    • Applied the Bessel-Legendre inequality to minimize result conservatism.
    • Established synchronization conditions for both partial and ordinary differential equation-based models.

    Main Results:

    • Achieved synchronization for reaction-diffusion complex dynamical networks with semi-Markov switching topology.
    • Demonstrated reduced data transmission through dynamic threshold parameters.
    • Ensured stochastic stability of the error system via derived synchronization conditions.
    • Validated the theoretical findings with two illustrative examples.

    Conclusions:

    • The proposed dynamic-memory event-triggered protocol effectively synchronizes stochastic jump CDNs.
    • The method offers improved control performance and reduced communication overhead.
    • The findings are applicable to both PDE- and ODE-based complex dynamical network models.