Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis

Abstract

In this paper, we focus on the global asymptotic stability problem for Clifford-valued neural network models with time-varying delays as well as impulsive effects. By considering impulsive effects, a general class of network model is considered, which encompasses real-valued, complex-valued, and quaternion-valued neural network models as special cases. Firstly, the n-dimensional Clifford-valued model is decomposed into 2mn-dimensional real-valued model, which avoids non-commutativity of multiplication of Clifford numbers. Based on the Lyapunov stability theory, contraction mapping principle, and some mathematical concepts, we derive the existence, uniqueness of the equilibrium point with respect to the model. New sufficient conditions are also derived, in order to ensure the global asymptotic stability of the considered model. To illustrate the usefulness of the obtained results, a simulation example is presented.