Global attracting set and asymptotic behavior for a class of impulsive functional Hopfield neural networks by a novel vector inequality

This article is concerned with a class of nonlinear and nonautonomous functional Hopfield neural networks with impulsive effects. The existence of attracting set and invariant set of the desired impulsive differential equations is established. Firstly, we construct a novel vector inequality, which considers the features of M-matrix. Based on the more general vector inequality, we ensure the positive invariant set and global attracting set for a class of the impulsive functional differential equations. By means of numerical simulation, the effectiveness of our theoretical results is demonstrated.