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Stability analysis of quaternion-valued neural networks with both discrete and distributed delays

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  • Tu, Zhengwen
  • Zhao, Yongxiang
  • Ding, Nan
  • Feng, Yuming
  • Zhang, Wei

Abstract

The existence, uniqueness and stability of the equilibrium of quaternion-valued neural networks (QVNNs) with both discrete and distributed delays are investigated in this paper. The considered model is managed as a single entirety without decomposition. Based on homeomorphic mapping theorem and linear matrix inequality, several sufficient criteria are derived to ascertain the aforementioned QVNNs to be globally asymptotically stable and exponentially stable. Moreover, provided criteria can be verified by the linear matrix inequality (LMI) toolbox in MATLAB. Finally, one simulation example is demonstrated to verify the effectiveness of obtained results.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:342-353
    DOI: 10.1016/j.amc.2018.09.049
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    References listed on IDEAS

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    1. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
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    1. Li, Hong-Li & Zhang, Long & Hu, Cheng & Jiang, Haijun & Cao, Jinde, 2020. "Global Mittag-Leffler synchronization of fractional-order delayed quaternion-valued neural networks: Direct quaternion approach," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    2. 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.
    3. Rajchakit, G. & Sriraman, R. & Lim, C.P. & Unyong, B., 2022. "Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 508-527.
    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. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks," Mathematics, MDPI, vol. 8(5), pages 1-27, May.
    6. Zhang, Weiwei & Sha, Chunlin & Cao, Jinde & Wang, Guanglan & Wang, Yuan, 2021. "Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    7. Baluni, Sapna & Sehgal, Ishani & Yadav, Vijay K. & Das, Subir, 2024. "Exponential synchronization of a class of quaternion-valued neural network with time-varying delays: A Matrix Measure Approach," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    8. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin & Wu, Tao & Zhang, Haiyang, 2021. "Stochastic stabilization of Markov jump quaternion-valued neural network using sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    9. Xue, Huanbin & Xu, Xiaohui & Zhang, Jiye & Yang, Xiaopeng, 2019. "Robust stability of impulsive switched neural networks with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 456-475.
    10. 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.
    11. 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).
    12. 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).
    13. Pan, Jie & Pan, Zhaoya, 2021. "Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    14. 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.
    15. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability," Mathematics, MDPI, vol. 8(5), pages 1-26, May.
    16. Grienggrai Rajchakit & Pharunyou Chanthorn & Pramet Kaewmesri & Ramalingam Sriraman & Chee Peng Lim, 2020. "Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks," Mathematics, MDPI, vol. 8(3), pages 1-29, March.
    17. 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).
    18. 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.
    19. Li, Hong-Li & Kao, Yonggui & Hu, Cheng & Jiang, Haijun & Jiang, Yao-Lin, 2021. "Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    20. Li, Donghua & Zhang, Zhengqiu & Zhang, Xiaoluan, 2020. "Periodic solutions of discrete-time Quaternion-valued BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    21. Jie Pan & Lianglin Xiong, 2021. "Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method," Mathematics, MDPI, vol. 9(11), pages 1-14, June.

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