Dynamic Analysis of Hybrid Impulsive Delayed Neural Networks With Uncertainties

Neural networks (NNs) have emerged as a powerful illustrative diagram for the brain. Unveiling the mechanism of neural-dynamic evolution is one of the crucial steps toward understanding how the brain works and evolves. Inspired by the universal existence of impulses in many real systems, this paper formulates a type of hybrid NNs (HNNs) with impulses, time delays, and interval uncertainties, and studies its global dynamic evolution by a robust interval analysis. The HNNs incorporate both continuous-time implementation and impulsive jump in mutual activations, where time delays and interval uncertainties are represented simultaneously. By constructing a Banach contraction mapping, the existence and uniqueness of the equilibrium of the HNN model are proved and analyzed in detail. Based on nonsmooth Lyapunov functions and delayed impulsive differential equations, new criteria are derived for ensuring the global robust exponential stability of the HNNs. Convergence analysis together with illustrative examples show the effectiveness of the theoretical results.

I. Introduction

Neural networks (NNs) have an integrated ability of efficient computation and evolving intelligence that have stimulated a great deal of research endeavor onto enabling them for high-performance learning, control, and optimization [1]–[4]. During the past three decades, tremendous efforts have been devoted to basic theories and real applications of NNs [5]–[8]. Various types of NN architectures have been built on solid mathematical and engineering theories, as well as fundamental principles that govern biological neural systems, including recurrent NNs, cellular NNs, Hopfield NNs, impulsive NNs, and delayed NNs [9]–[11], [13], [18], [19]. For instance, Hopfield NNs are formulated and analyzed in [1]; stability of delayed Hopfield NNs is investigated in [6], [24], [34]; dynamical behaviors of delayed recurrent NNs are studied in [7], [8], [28], and [30].