说明：   本文将介绍Hopfield神经网络(HNN)的产生、发展及基本原理，重点是对离散Hopfield网络(DHNN)的说明。包括：网络结构、涉及的算法和神经网络的训练方法；具体实例描述网络的联想去噪功能；进行计算机仿真计算及仿真结果说明；仿真程序的说明文档（仿真程序附后）；最后将对DHNN的最新发展状况作简单阐述。
(This article will introduce the Hopfield neural network (HNN) production, development and the basic principles of focus on the discrete Hopfield network (DHNN) note. Including: network infrastructure, involving algorithms and neural network training methods concrete examples to describe the network Lenovo denoising function to carry out computer simulation calculation and simulation results show Simulation Program documentation (simulation program is attached) final will DHNN the latest developments in the situation described briefly.)