發(fā)布時間：2018-04-30 17:38

  本文選題：分段連續(xù) + 漸近周期��； 參考：《延邊大學(xué)》2015年碩士論文

【摘要】：神經(jīng)網(wǎng)絡(luò)是一門新興的綜合性,交叉性很強(qiáng)的學(xué)科.近二十年來,國內(nèi)外許多學(xué)者建立了大量的神經(jīng)網(wǎng)絡(luò)模型,如：雙向聯(lián)想記憶神經(jīng)網(wǎng)絡(luò)模型、Hopfield神經(jīng)網(wǎng)絡(luò)模型、細(xì)胞神經(jīng)網(wǎng)絡(luò)模型等,這些神經(jīng)網(wǎng)絡(luò)模型已成功地應(yīng)用于工程技術(shù),物理學(xué),經(jīng)濟(jì)學(xué)等許多領(lǐng)域.在神經(jīng)網(wǎng)絡(luò)的研究中時滯神經(jīng)網(wǎng)絡(luò)的動力學(xué)性質(zhì),如穩(wěn)定性、不穩(wěn)定性、振動性和混沌行為等最近已成為了重要的研究課題,并吸引了許多國內(nèi)外學(xué)者的關(guān)注.眾所周知,大部分人工神經(jīng)網(wǎng)絡(luò)模型可以用微分方程、差分方程的定性理論來描述,因此,微分方程、差分方程的定性理論的設(shè)計和應(yīng)用在人工神經(jīng)網(wǎng)絡(luò)上起到重要作用.目前,關(guān)于神經(jīng)網(wǎng)絡(luò)模型的周期解的存在性、穩(wěn)定性及吸引性等方面的研究有了大量的研究成果.但非線性神經(jīng)網(wǎng)絡(luò)模型的解的漸近性研究的相對較少,尤其是帶有分段連續(xù)控制項的神經(jīng)網(wǎng)絡(luò)模型的研究成果較少.本文主要研究如下形式的非線性差分方程其中{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 滿足這里λ∈(0,+∞),我們可把方程(1)可視為非線性神經(jīng)網(wǎng)絡(luò)模型.通過變換xn(i)=x(2κ+1)n+i,(n,i)∈N×{0,1,···,2κ}∪{-1}×{2κ-1,2κ},(1)可轉(zhuǎn)化如下的2κ+1—維自治動力系統(tǒng)全文共分三章：第一章,引言部分,我主要陳述了研究神經(jīng)網(wǎng)絡(luò)的背景及發(fā)展現(xiàn)狀,介紹了一些有關(guān)神經(jīng)網(wǎng)絡(luò)模型的研究成果以及本文的主要工作；第二章,引入一些基本的定義及相關(guān)的符號的說明；第三章,主要研究了當(dāng)閾值在不同的取值范圍時,解的漸近周期性,通過分析(2)獲得了(1)的完全漸近性.
[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，

本文編號：1825529