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Exponential stability of impulsive complex-valued neural networks with time delay

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  • Wang, Zengyun
  • Liu, Xinzhi

Abstract

This paper studies the stability problem of impulsive complex-valued neural networks with time delay. Firstly, impulses are viewed as disturbance. Criteria on uniqueness and global exponential stability of equilibrium point are established using the Lyapunov function method. A modified version of Halanay-type inequality is used to make the results in Song et al. (2016) much better. Secondly, impulses are used as control input. Sufficient conditions are derived to ensure the exponential stability of the equilibrium point by using the Razumikhin technique. This result explains the dynamics of example 2 in Song et al. (2016), which does not give any theoretical result on impulsive control problem. Two numerical examples are presented to demonstrate the effectiveness of the theorems.

Suggested Citation

  • Wang, Zengyun & Liu, Xinzhi, 2019. "Exponential stability of impulsive complex-valued neural networks with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 143-157.
    • Handle: RePEc:eee:matcom:v:156:y:2019:i:c:p:143-157
    DOI: 10.1016/j.matcom.2018.07.006
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    References listed on IDEAS

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    1. Yang, Rongjiang & Wu, Bo & Liu, Yang, 2015. "A Halanay-type inequality approach to the stability analysis of discrete-time neural networks with delays," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 696-707.
    2. Tao Fang & Jitao Sun, 2013. "Stability Analysis of Complex-Valued Nonlinear Differential System," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
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    Cited by:

    1. Zhang, Chunmei & Han, Bang-Sheng, 2020. "Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. 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.
    3. Zou, Cong & Li, Bing & Liu, Feiyang & Xu, Bingrui, 2022. "Event-Triggered μ-state estimation for Markovian jumping neural networks with mixed time-delays," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    4. Sriraman, R. & Cao, Yang & Samidurai, R., 2020. "Global asymptotic stability of stochastic complex-valued neural networks with probabilistic time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 103-118.
    5. Duan, Wenyong & Li, Yan & Sun, Yi & Chen, Jian & Yang, Xiaodong, 2020. "Enhanced master–slave synchronization criteria for chaotic Lur’e systems based on time-delayed feedback control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 276-294.
    6. Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution and extinction of a stochastic ratio-dependent predator–prey system with stage structure for the predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. Duan, Lian & Shi, Min & Huang, Chuangxia & Fang, Xianwen, 2021. "Synchronization in finite-/fixed-time of delayed diffusive complex-valued neural networks with discontinuous activations," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Yujuan Tian & Yuhan Yin & Fei Wang & Kening Wang, 2022. "Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    9. Fan, Hongguang & Shi, Kaibo & Zhao, Yi, 2022. "Global μ-synchronization for nonlinear complex networks with unbounded multiple time delays and uncertainties via impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).

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