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Novel Synchronization Conditions for the Unified System of Multi-Dimension-Valued Neural Networks

Author

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  • Jianying Xiao

    (School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu 610106, China
    Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China)

  • Yongtao Li

    (College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610050, China)

Abstract

This paper discusses the novel synchronization conditions about the unified system of multi-dimension-valued neural networks (USOMDVNN). First of all, the general model of USOMDVNN is successfully set up, mainly on the basis of multidimensional algebra, Kirchhoff current law, and neuronal property. Then, the concise Lyapunov–Krasovskii functional (LKF) and switching controllers are constructed for the USOMDVNN. Moreover, the new inequalities, whose variables, together with some parameters, are employed in a concise and unified form whose variables can be translated into special ones, such as real, complex, and quaternion. It is worth mentioning that the useful parameters really make some contributions to the construction of the concise LKF, the design of the general controllers, and the acquisition of flexible criteria. Further, we acquire the newer criteria mainly by employing Lyapunov analysis, constructing new LKF, applying two unified inequalities, and designing nonlinear controllers. Particularly, the value of the fixed time is less than the other ones in some existing results, owing to the adjustable parameters. Finally, three multidimensional simulations are presented, to demonstrate the availability and progress of the achieved acquisitions.

Suggested Citation

  • Jianying Xiao & Yongtao Li, 2022. "Novel Synchronization Conditions for the Unified System of Multi-Dimension-Valued Neural Networks," Mathematics, MDPI, vol. 10(17), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3031-:d:895143
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    References listed on IDEAS

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    1. Li, Hui & Kao, Yonggui & Li, Hong-Li, 2021. "Globally β-Mittag-Leffler stability and β-Mittag-Leffler convergence in Lagrange sense for impulsive fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun & Huang, Junjian, 2018. "Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 105-123.
    3. Arbi, Adnène, 2021. "Novel traveling waves solutions for nonlinear delayed dynamical neural networks with leakage term," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Pharunyou Chanthorn & Grienggrai Rajchakit & Jenjira Thipcha & Chanikan Emharuethai & Ramalingam Sriraman & Chee Peng Lim & Raja Ramachandran, 2020. "Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    5. Vadivel, R. & Hammachukiattikul, Porpattama & Rajchakit, G. & Syed Ali, M. & Unyong, Bundit, 2021. "Finite-time event-triggered approach for recurrent neural networks with leakage term and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 765-790.
    6. Aadhithiyan, S. & Raja, R. & Zhu, Q. & Alzabut, J. & Niezabitowski, M. & Lim, C.P., 2021. "Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    7. Zhang, Wanli & Li, Chuandong & Huang, Tingwen & Huang, Junjian, 2018. "Fixed-time synchronization of complex networks with nonidentical nodes and stochastic noise perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1531-1542.
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