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

Wenjun Dong, Yujiao Huang, Tingan Chen, Xinggang Fan and Haixia Long
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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

Mathematics, 2022, vol. 10, issue 13, 1-21

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.

Keywords: quaternion-valued neural network; local Lagrange exponential stability; multiple equilibrium points; time delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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