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Fixed-Time Synchronization of Reaction-Diffusion Fuzzy Neural Networks with Stochastic Perturbations

Author

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  • Hayrengul Sadik

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)

  • Abdujelil Abdurahman

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)

  • Rukeya Tohti

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)

Abstract

In this paper, we investigated the fixed-time synchronization problem of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations by developing simple control schemes. First, some generalized fixed-time stability results are introduced for stochastic nonlinear systems. Based on these results, some generic fixed-time stability criteria are established and upper bounds of settling time are directly calculated by using several special functions. Then, the fixed-time synchronization of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations is analysed by designing a type of controller which is more simple and thus have a better applicability. Finally, one numerical example with its Matlab simulations is provided to show the feasibility of developed theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1493-:d:1101056
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    References listed on IDEAS

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    1. Abudusaimaiti, Mairemunisa & Abdurahman, Abdujelil & Jiang, Haijun & Hu, Cheng, 2022. "Fixed/predefined-time synchronization of fuzzy neural networks with stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. Weiyuan Zhang & Junmin Li & Minglai Chen, 2012. "Dynamical Behaviors of Impulsive Stochastic Reaction-Diffusion Neural Networks with Mixed Time Delays," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-21, August.
    3. Lu, Jun Guo, 2008. "Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 116-125.
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    Cited by:

    1. 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.
    2. Yupeng Shi & Dayong Ye, 2023. "Stability Analysis of Delayed Neural Networks via Composite-Matrix-Based Integral Inequality," Mathematics, MDPI, vol. 11(11), pages 1-13, May.

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