# Delayed Hybrid Impulsive Neural Networks

## Abstract

This chapter first introduces the continuous-time Hopfield neural networks. The existence and uniqueness of equilibrium, as well as its stability and instability, of continuous-time Hopfield networks are analyzed, and less conservative yet more general results are established. Then, in light of the continuous-time architecture of Hopfield networks, the impulsive Hopfield neural networks with transmission delays are formulated and explained. Many evolutionary processes, particularly biological systems, that exhibit impulsive dynamical behaviors, can be described by the impulsive Hopfield neural networks. Fundamental issues such as the global exponential stability, the existence and uniqueness of the equilibrium of such impulsive Hopfield networks are established. A numerical example is given for illustration and interpretation of the theoretical results.

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