【作者】 徐军；

【导师】 钟守铭；

【作者基本信息】 电子科技大学 ， 运筹学与控制论， 2004， 硕士

【摘要】 本文主要研究的是无时滞和有时滞Hopfield型神经网络的稳定性。第一章首先介绍连续型Hopfield神经网络参数及其工作机理,随后运用现代数学方法讨论了Hopfield型神经网络的平衡点的存在与唯一性问题。最后采用李雅普诺夫直接法,并结合运用M矩阵理论研究了Hopfield型神经网络的全局渐近稳定性。第二章研究的是具有分布时滞的Hopfield型神经网络的稳定性。首先运用Brouwer不动点定理,研究了具有分布时滞的常系数Hopfield型神经网络的平衡点的存在性。随后采用李雅普诺夫函数方法,并运用了推广的Halanay时滞微分不等式分别研究了分布时滞的常系数和变系数Hopfield型神经网络的稳定性。第三章根据李雅普诺夫泛函方法,运用了一种全新的方法研究了时滞细胞神经网络的稳定性,随后又根据这一方法分别讨论了无时滞和有时滞的Hopfield型神经网络的稳定性。更多还原

【Abstract】 This dissertation mainly studies the stability of Hopfield Neural Networks and consists of three chapters. In chapter 1, the structure and the parameter of continuous Hopfield Neural Networks are introduced. Then the existence and uniqueness of the balance point is studied with the modern mathematics methods. Finally, the global asymptotic stability of the networks is studied with Lyapunov Direct Method. During the proof, the M-matrix theory is used. In chapter 2, the stability of distributed delayed Hopfield Neural Networks is studied. Firstly, the existence of the balance point is studied with Brouwer Fixed Point Theorem. Then the stability of both constant coefficient distributed delayed Hopfield Neural Networks and variable coefficient distributed delayed Hopfield Neural Networks are studied with Lyapunov Function Method. During the proof, the delayed Halanay differential inequality is used. In chapter 3, the Lyapunov functional based new method is used to study the Delayed Cellular Neural Networks. Then with the same method, both the Delayed Hopfield Neural Networks and Hopfield Neural Networks without delay are studied.更多还原