Effect of Impulses on Robust Exponential Stability of Delayed Quaternion-Valued Neural Networks.

This paper investigates the dynamic behavior of a class of delayed quaternion-valued neural networks (QVNNs) with impulses and parameter uncertainties. First, we assume that the activation function and connection matrices in the model are defined in the quaternion domain. Without decomposing the QVNNs into four equivalent neural networks in a real number domain or two equivalent neural networks in a complex number domain, the existence and uniqueness of the equilibrium point (EP) are studied based on the M-matrix and homeomorphism mapping theories. By combing the vector Lyapunov function with mathematical induction, theorems are given to ensure robust exponential stability of the system's EP. The results reflect the influence of connection matrices, delays, impulses, and the activation function on the convergence speed of the EP. Finally, the feasibility of the derived results is explained through three examples. [ABSTRACT FROM AUTHOR]