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Stochastic Synchronization of Impulsive Reaction–Diffusion BAM Neural Networks at a Fixed and Predetermined Time

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  • Rouzimaimaiti Mahemuti

    (School of Information Technology and Engineering, Guangzhou College of Commerce, Guangzhou 511363, China
    Guangdong Provincial Key Laboratory of Computational Science and Material Design, Southern University of Science and Technology, Shenzhen 518055, China)

  • Ehmet Kasim

    (College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China)

  • Hayrengul Sadik

    (College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China)

Abstract

This paper discusses the synchronization problem of impulsive stochastic bidirectional associative memory neural networks with a diffusion term, specifically focusing on the fixed-time (FXT) and predefined-time (PDT) synchronization. First, a number of more relaxed lemmas are introduced for the FXT and PDT stability of general types of impulsive nonlinear systems. A controller that does not require a sign function is then proposed to ensure that the synchronization error converges to zero within a predetermined time. The controllerdesigned in this paper serves the additional purpose of preventing the use of an unreliable inequality in the course of proving the main results. Next, to guarantee FXT and PDT synchronization of the drive–response systems, this paper employs the Lyapunov function method and derives sufficient conditions. Finally, a numerical simulation is presented to validate the theoretical results.

Suggested Citation

  • Rouzimaimaiti Mahemuti & Ehmet Kasim & Hayrengul Sadik, 2024. "Stochastic Synchronization of Impulsive Reaction–Diffusion BAM Neural Networks at a Fixed and Predetermined Time," Mathematics, MDPI, vol. 12(8), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1204-:d:1377445
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    References listed on IDEAS

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    3. Abdurahman, Abdujelil & Abudusaimaiti, Mairemunisa & Jiang, Haijun, 2023. "Fixed/predefined-time lag synchronization of complex-valued BAM neural networks with stochastic perturbations," Applied Mathematics and Computation, Elsevier, vol. 444(C).
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    5. Sader, Malika & Abdurahman, Abdujelil & Jiang, Haijun, 2018. "General decay synchronization of delayed BAM neural networks via nonlinear feedback control," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 302-314.
    6. Hayrengul Sadik & Abdujelil Abdurahman & Rukeya Tohti, 2023. "Fixed-Time Synchronization of Reaction-Diffusion Fuzzy Neural Networks with Stochastic Perturbations," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
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