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Stability analysis for BAM quaternion-valued inertial neural networks with time delay via nonlinear measure approach

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  • Liu, Jin
  • Jian, Jigui
  • Wang, Baoxian

Abstract

In this paper, the global stability for BAM quaternion-valued inertial neural networks with time delay is investigated without transforming the inertial terms into first order by some variable substitutions. To avoid the non-commutativity of quaternion multiplication, the discussed system is transformed into four real-valued models. Based on nonlinear measure approach and some inequality techniques, a new sufficient condition is obtained to ensure the existence and uniqueness of the equilibrium point. Meanwhile, some new Lyapunov functionals are constructed to directly propose the asymptotic stability for the discussed system and some new stability criteria in linear matrix inequality form are derived by means of Barbalat Lemma and inequality techniques. It is worth mentioning that this paper directly analyzes the dynamic performance of the concerned system, which is different from the traditional reduced-order variable replacement method. Finally, some numerical examples with simulations are given to demonstrate the validity of the theoretical results.

Suggested Citation

  • Liu, Jin & Jian, Jigui & Wang, Baoxian, 2020. "Stability analysis for BAM quaternion-valued inertial neural networks with time delay via nonlinear measure approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 134-152.
    • Handle: RePEc:eee:matcom:v:174:y:2020:i:c:p:134-152
    DOI: 10.1016/j.matcom.2020.03.002
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    References listed on IDEAS

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    Cited by:

    1. Chen, Dazhao & Zhang, Zhengqiu, 2022. "Finite-time synchronization for delayed BAM neural networks by the approach of the same structural functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
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    3. 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.
    4. Zhang, Zhengqiu & Yang, Zhen, 2023. "Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin, 2022. "Stochastic stability criteria and event-triggered control of delayed Markovian jump quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 420(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).
    7. 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).

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