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Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis

Author

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  • Rajchakit, G.
  • Sriraman, R.
  • Vignesh, P.
  • Lim, C.P.

Abstract

In this paper, we focus on the global asymptotic stability problem for Clifford-valued neural network models with time-varying delays as well as impulsive effects. By considering impulsive effects, a general class of network model is considered, which encompasses real-valued, complex-valued, and quaternion-valued neural network models as special cases. Firstly, the n-dimensional Clifford-valued model is decomposed into 2mn-dimensional real-valued model, which avoids non-commutativity of multiplication of Clifford numbers. Based on the Lyapunov stability theory, contraction mapping principle, and some mathematical concepts, we derive the existence, uniqueness of the equilibrium point with respect to the model. New sufficient conditions are also derived, in order to ensure the global asymptotic stability of the considered model. To illustrate the usefulness of the obtained results, a simulation example is presented.

Suggested Citation

  • Rajchakit, G. & Sriraman, R. & Vignesh, P. & Lim, C.P., 2021. "Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    • Handle: RePEc:eee:apmaco:v:407:y:2021:i:c:s0096300321003982
    DOI: 10.1016/j.amc.2021.126309
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    Cited by:

    1. Fei Luo & Weiyi Hu & Enli Wu & Xiufang Yuan, 2024. "Global Exponential Stability of Impulsive Delayed Neural Networks with Parameter Uncertainties and Reaction–Diffusion Terms," Mathematics, MDPI, vol. 12(15), pages 1-15, July.
    2. Shen, Shiping & Meng, Xiaofang, 2023. "Finite-time stability of almost periodic solutions of Clifford-valued RNNs with time-varying delays and D operator on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Li, Yongkun & Wang, Xiaohui, 2021. "Almost periodic solutions in distribution of Clifford-valued stochastic recurrent neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    4. Grienggrai Rajchakit & Ramalingam Sriraman & Chee Peng Lim & Panu Sam-ang & Porpattama Hammachukiattikul, 2021. "Synchronization in Finite-Time Analysis of Clifford-Valued Neural Networks with Finite-Time Distributed Delays," Mathematics, MDPI, vol. 9(11), pages 1-18, May.
    5. Weiwei Qi & Yongkun Li, 2022. "Almost Anti-Periodic Oscillation Excited by External Inputs and Synchronization of Clifford-Valued Recurrent Neural Networks," Mathematics, MDPI, vol. 10(15), pages 1-12, August.

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