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Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay

Author

Listed:
  • Jinlong Shu

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China)

  • Lianglin Xiong

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China)

  • Tao Wu

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China)

  • Zixin Liu

    (Department of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

Abstract

This paper addresses the problem of global μ -stability for quaternion-valued neutral-type neural networks (QVNTNNs) with time-varying delays. First, QVNTNNs are transformed into two complex-valued systems by using a transformation to reduce the complexity of the computation generated by the non-commutativity of quaternion multiplication. A new convex inequality in a complex field is introduced. In what follows, the condition for the existence and uniqueness of the equilibrium point is primarily obtained by the homeomorphism theory. Next, the global stability conditions of the complex-valued systems are provided by constructing a novel Lyapunov–Krasovskii functional, using an integral inequality technique, and reciprocal convex combination approach. The gained global μ -stability conditions can be divided into three different kinds of stability forms by varying the positive continuous function μ ( t ) . Finally, three reliable examples and a simulation are given to display the effectiveness of the proposed methods.

Suggested Citation

  • Jinlong Shu & Lianglin Xiong & Tao Wu & Zixin Liu, 2019. "Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay," Mathematics, MDPI, vol. 7(1), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:101-:d:199035
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    References listed on IDEAS

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    6. Took, C. Cheong & Strbac, G. & Aihara, K. & Mandic, D.P., 2011. "Quaternion-valued short-term joint forecasting of three-dimensional wind and atmospheric parameters," Renewable Energy, Elsevier, vol. 36(6), pages 1754-1760.
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    Cited by:

    1. Jun Guo & Yanchao Shi & Weihua Luo & Yanzhao Cheng & Shengye Wang, 2023. "Adaptive Global Synchronization for a Class of Quaternion-Valued Cohen-Grossberg Neural Networks with Known or Unknown Parameters," Mathematics, MDPI, vol. 11(16), pages 1-16, August.
    2. Juan Yu & Kailong Xiong & Cheng Hu, 2024. "Synchronization Analysis for Quaternion-Valued Delayed Neural Networks with Impulse and Inertia via a Direct Technique," Mathematics, MDPI, vol. 12(7), pages 1-22, March.

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