一类带有分段连续控制项的非线性递推关系的渐近周期性

发布时间：2018-04-30 17:38

  本文选题：分段连续 + 渐近周期　； 参考：《延边大学》2015年硕士论文

【摘要】：神经网络是一门新兴的综合性,交叉性很强的学科.近二十年来,国内外许多学者建立了大量的神经网络模型,如：双向联想记忆神经网络模型、Hopfield神经网络模型、细胞神经网络模型等,这些神经网络模型已成功地应用于工程技术,物理学,经济学等许多领域.在神经网络的研究中时滞神经网络的动力学性质,如稳定性、不稳定性、振动性和混沌行为等最近已成为了重要的研究课题,并吸引了许多国内外学者的关注.众所周知,大部分人工神经网络模型可以用微分方程、差分方程的定性理论来描述,因此,微分方程、差分方程的定性理论的设计和应用在人工神经网络上起到重要作用.目前,关于神经网络模型的周期解的存在性、稳定性及吸引性等方面的研究有了大量的研究成果.但非线性神经网络模型的解的渐近性研究的相对较少,尤其是带有分段连续控制项的神经网络模型的研究成果较少.本文主要研究如下形式的非线性差分方程其中{an}∞n=0,{bn}∞n=0是2κ+1—周期序列,其中αi∈(0,1),bi=1-αi,i=0,1,…,κ.f 满足这里λ∈(0,+∞),我们可把方程(1)可视为非线性神经网络模型.通过变换xn(i)=x(2κ+1)n+i,(n,i)∈N×{0,1,···,2κ}∪{-1}×{2κ-1,2κ},(1)可转化如下的2κ+1—维自治动力系统全文共分三章：第一章,引言部分,我主要陈述了研究神经网络的背景及发展现状,介绍了一些有关神经网络模型的研究成果以及本文的主要工作；第二章,引入一些基本的定义及相关的符号的说明；第三章,主要研究了当阈值在不同的取值范围时,解的渐近周期性,通过分析(2)获得了(1)的完全渐近性.
[Abstract]:Neural network is a new comprehensive and intersecting subject. In the past two decades, many scholars at home and abroad have established a large number of neural network models, such as two-way associative memory neural network model, hopfield neural network model, cellular neural network model and so on. These neural network models have been successfully applied in many fields, such as engineering, physics, economics and so on. In the research of neural networks, the dynamical properties of delayed neural networks, such as stability, instability, oscillation and chaotic behavior, have recently become an important research topic, and attracted the attention of many scholars at home and abroad. As we all know, most artificial neural network models can be described by the qualitative theory of differential equation and difference equation. Therefore, the design and application of qualitative theory of differential equation and difference equation play an important role in artificial neural network. At present, there have been a lot of research results on the existence, stability and attraction of periodic solutions of neural network models. However, there are few researches on the asymptotic behavior of the nonlinear neural network model, especially on the neural network model with piecewise continuous control term. In this paper, the following forms of nonlinear difference equations are studied, where {an} 鈭，

本文编号：1825529