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

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(4n) subregions, and using the intermediate value theorem, sufficient conditions are proposed to ensure quaternion-valued neural networks have 3(4n) equilibrium points. According to the Halanay inequality, the conditions for the existence of 2(4n) 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.

Automated summary

This study examines the local stability of quaternion-valued neural networks, which is crucial for the application of associative memory and pattern recognition. The research proposes conditions to ensure the existence of multiple equilibrium points and stable equilibria in quaternion-valued neural networks, improving and extending the existing results.