摘要
摘 要
神经网络在神经生理学、神经解剖学的范畴内，指的是生物神经未网络；在 信息计算机科学等领域内，指的是向生命学习而构造的人工神经网络。 神经网 络的研究实质是 ANN 向 BNN 学习的问题；1982 年，美国加州理工学院生物 物理学家 Hopfield 提出了神经网络的模型－Hopfield 神经网络模型，有力的推 动了神经网络理论的研究，同时 Hopfield 还引入“计算能量函数”的概念，给出 了网络稳定性的判据和电子电路实现，为神经计算机的研究奠定了基础。 人工神经网络是模拟生物脑结构和功能的一种信息处理系统， 虽然目前的模 仿正处于低级水平，但已经显出一些与生物类似的特点：大规模并行结构，信息 的分布式存储和并行处理，具有良好的自适应性，自组织性和容错性，具有较强 的学习、记忆、识别功能等等。 神经网络系统的理论和实践中， 神经网络的稳定性始终是一个至关重要的问 题。一个好的 Hopfield 神经网络系统具有稳定性好、对各类输入能产生响应等 特性。因此 Hopfield 神经网络系统具有较好的理论和实践意义。本文讨论了无 时滞神经网络和时滞神经网络的稳定性。 关键词：神经网络、Lyapunov 函数、不等式分析、Dini 导数 NhomakorabeaII
目录
目 录
第 1 章 绪论.................................................................................................................. 1 1.1 人工神经网络简介............................................................................................ 1 1.2 人工神经网络的应用...................................................................................... 1 1.3 动力学系统中的稳定性概念............................................................................ 2 1.4 Hopfield 神经网络的产生及其意义.............................................................. 2 第 2 章 无时滞 HNN 稳定性........................................................................................ 4 2.1 连续 HNN 模型.................................................................................................. 4 2.1.1 连续 HNN 模型.......................................................................................... 4 2.1.2 关于连续 HNN 模型的讨论...................................................................... 6 2.2 平衡点的存在与唯一性问题............................................................................ 7 2.2.1 预备知识.................................................................................................... 7 2.3 第3章 3.2 平衡点的全局渐近稳定性............................................................................ 10 一阶二阶 Hopfield 神经网络的稳定性.................................................... 15 具有时滞的二阶 Hopfield 神经网络........................................................ 22
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ABSTRACT
ABSTRACT
Neural networks mean Biological Neural Networks in the category of neuro inphysiology and neural anatomy and call Artificial Neural Networks the field of information computer science,etc. The research essence of the neural network is that ANN is learn from BNN, In 1982, biological physicist Hopfield of California Institute of Technology of U.S.A. proposed the model of the neural network the neural network model of Hopfield, push the research of neural network. At the same time Hopfield still introduces the concept of " calculating energy function ", provide the criterion of the stability of the neural network and realize of electronic circuit and have established the foundation for the research of the neural computer. In theory and practice of neural networks system, Hopfield neural networks system is a very important problem all the time. A good Hopfield neural networks system have characteristics of a good stability and product respond of all kinds of input.Thus Hopfield neural networks system have better meaning of theory and practise. This text discussing stability of non-delay neural networks system and delay neural networks system. This text divides four chapters: Chapter one is foreword,main introduct selected title background of this text.Chapter two discuss exponential stability of non-delay recurrent neural networks. Chapter three introduct delay neural networks with time arying. Chapter four study stability of delay cell neural networks Key Words:Neural networks, Lyapunov function, Inequality analysis, Dini derivative
3.1 具有时滞的 Hopfield 神经网络.................................................................. 15 3.2.1 模型描述.................................................................................................. 22 3.2.2 平衡点的存在性和唯一性...................................................................... 23 3.3 具有时滞的二阶 Hopfield 神经网络.......................................................... 25 第4章 总结与展望.................................................................................................. 27 参考文献...................................................................................................................... 28 致谢.............................................................................................................................. 29 外文资料原文.............................................................................................................. 30 外文资料译文.............................................................................................................. 37