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Global exponential convergence for impulsive inertial complex-valued neural networks with time-varying delays

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  • Tang, Qian
  • Jian, Jigui

Abstract

This paper focuses on the exponential convergence of impulsive inertial complex-valued neural networks with time-varying delays. The system can be expressed as a first order differential equation by selecting a proper variable substitution. By constructing proper Lyapunov–Krasovskii functionals and using inequality techniques, some delay-dependent sufficient conditions in linear matrix inequality form are proposed to ascertain the global exponential convergence of the addressed neural networks with two classes of complex-valued activation functions. The framework of the exponential convergence ball domain in which all trajectories converge is also given. Meanwhile, the obtained results here do not meet that the derivatives of the time-varying delays are less than one and there are also no limit to the strength of impulses. The methods here can also be applied to deal with multistable and monostable neural networks because of making no hypotheses on the amount of the equilibrium points. Finally, two examples are given to demonstrate the validity of the theoretical results.

Suggested Citation

  • Tang, Qian & Jian, Jigui, 2019. "Global exponential convergence for impulsive inertial complex-valued neural networks with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 39-56.
    • Handle: RePEc:eee:matcom:v:159:y:2019:i:c:p:39-56
    DOI: 10.1016/j.matcom.2018.10.009
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    1. Chen, Xiaofeng & Zhao, Zhenjiang & Song, Qiankun & Hu, Jin, 2017. "Multistability of complex-valued neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 18-35.
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    Cited by:

    1. Yaning Yu & Ziye Zhang, 2022. "State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    2. Iswarya, M. & Raja, R. & Cao, J. & Niezabitowski, M. & Alzabut, J. & Maharajan, C., 2022. "New results on exponential input-to-state stability analysis of memristor based complex-valued inertial neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 440-461.
    3. Peng, Qiu & Jian, Jigui, 2023. "Synchronization analysis of fractional-order inertial-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 62-77.
    4. Zhao, Rui & Wang, Baoxian & Jian, Jigui, 2022. "Global μ-stabilization of quaternion-valued inertial BAM neural networks with time-varying delays via time-delayed impulsive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 223-245.
    5. Pan, Jinsong & Zhang, Zhengqiu, 2021. "Finite-time synchronization for delayed complex-valued neural networks via the exponential-type controllers of time variable," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Kumar, Ankit & Das, Subir & Singh, Sunny & Rajeev,, 2023. "Quasi-projective synchronization of inertial complex-valued recurrent neural networks with mixed time-varying delay and mismatched parameters," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    7. Bao, Gang & Zeng, Zhigang, 2021. "Prescribed convergence analysis of recurrent neural networks with parameter variations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 858-870.
    8. Wei, Xiaofeng & Zhang, Ziye & Lin, Chong & Chen, Jian, 2021. "Synchronization and anti-synchronization for complex-valued inertial neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    9. Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    10. Han, Siyu & Hu, Cheng & Yu, Juan & Jiang, Haijun & Wen, Shiping, 2021. "Stabilization of inertial Cohen-Grossberg neural networks with generalized delays: A direct analysis approach," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    11. Lin, Dongyuan & Chen, Xiaofeng & Yu, Guoping & Li, Zhongshan & Xia, Yannan, 2021. "Global exponential synchronization via nonlinear feedback control for delayed inertial memristor-based quaternion-valued neural networks with impulses," Applied Mathematics and Computation, Elsevier, vol. 401(C).

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