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Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks

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  • Wang, Huamin
  • Wei, Guoliang
  • Wen, Shiping
  • Huang, Tingwen

Abstract

In reality, abrupt uncertainty phenomenon may disturb or even break the system stability. Under these circumstances, it is worthy of studying the stability criteria of impulsive disturbed systems. In this article, an impulsive disturbed neural network model with delays is constructed in quaternion space, and the exponential stability conditions of the delayed system are derived by utilizing generalized norms. Firstly, a general impulsive disturbed quaternion-valued delayed neural network (IQVDNN) is given by combining impulsive differential system with quaternion-valued neural networks. Since quaternion multiplication is noncommutative, the IQVDNN system is decomposed into real-valued impulsive delayed neural networks. Then, the generalized ∞-norm and 1-norm are used to research its stability, respectively. By constructing special Lyapunov-type functional, several exponential stability sufficient criteria are obtained, which can guarantee that the stability can’t be destroyed by abrupt impulsive perturbations. Finally, two numerical examples and their simulation figures are given to show the effectiveness of the obtained conclusions.

Suggested Citation

  • Wang, Huamin & Wei, Guoliang & Wen, Shiping & Huang, Tingwen, 2021. "Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320306330
    DOI: 10.1016/j.amc.2020.125680
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    References listed on IDEAS

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    1. Pahnehkolaei, Seyed Mehdi Abedi & Alfi, Alireza & Machado, J.A. Tenreiro, 2019. "Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 278-293.
    2. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Tu, Zhengwen & Zhao, Yongxiang & Ding, Nan & Feng, Yuming & Zhang, Wei, 2019. "Stability analysis of quaternion-valued neural networks with both discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 342-353.
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    Cited by:

    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. Qingchao Meng & Huamin Wang, 2023. "Impulsive Destabilization Effect on Novel Existence of Solution and Global μ -Stability for MNNs in Quaternion Field," Mathematics, MDPI, vol. 11(8), pages 1-12, April.
    3. Feng, Likang & Zhang, Weihai & Wu, Zhaojing, 2023. "Noise-to-state stability of random impulsive delay systems with multiple random impulses," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    4. Yu, Siyi & Li, Hua & Chen, Xiaofeng & Lin, Dongyuan, 2023. "Multistability analysis of quaternion-valued neural networks with cosine activation functions," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    5. Shang, Weiying & Zhang, Weiwei & Chen, Dingyuan & Cao, Jinde, 2023. "New criteria of finite time synchronization of fractional-order quaternion-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    6. Xiong, Kailong & Hu, Cheng & Yu, Juan, 2023. "Direct approach-based synchronization of fully quaternion-valued neural networks with inertial term and time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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