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Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays

Author

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  • Wenjun Dong

    (College of Zhijiang, Zhejiang University of Technology, Shaoxing 312030, China)

  • Yujiao Huang

    (College of Zhijiang, Zhejiang University of Technology, Shaoxing 312030, China)

  • Tingan Chen

    (College of Zhijiang, Zhejiang University of Technology, Shaoxing 312030, China)

  • Xinggang Fan

    (College of Zhijiang, Zhejiang University of Technology, Shaoxing 312030, China)

  • Haixia Long

    (College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310058, China)

Abstract

This study on the local stability of quaternion-valued neural networks is of great significance to the application of associative memory and pattern recognition. In the research, we study local Lagrange exponential stability of quaternion-valued neural networks with time delays. By separating the quaternion-valued neural networks into a real part and three imaginary parts, separating the quaternion field into 3 4 n subregions, and using the intermediate value theorem, sufficient conditions are proposed to ensure quaternion-valued neural networks have 3 4 n equilibrium points. According to the Halanay inequality, the conditions for the existence of 2 4 n local Lagrange exponentially stable equilibria of quaternion-valued neural networks are established. The obtained stability results improve and extend the existing ones. Under the same conditions, quaternion-valued neural networks have more stable equilibrium points than complex-valued neural networks and real-valued neural networks. The validity of the theoretical results were verified by an example.

Suggested Citation

  • Wenjun Dong & Yujiao Huang & Tingan Chen & Xinggang Fan & Haixia Long, 2022. "Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays," Mathematics, MDPI, vol. 10(13), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2157-:d:843756
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    References listed on IDEAS

    as
    1. Wang, Shuzhan & Zhang, Ziye & Lin, Chong & Chen, Jian, 2021. "Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    2. 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).
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