本文關鍵詞： 時滯細胞神經網絡 指數穩(wěn)定性 漸近穩(wěn)定性 以分布漸近穩(wěn)定性 漸近同步性 Lyapunov泛函　出處：《天津師范大學》2015年碩士論文　論文類型：學位論文

【摘要】：時滯細胞神經網絡是一大規(guī)模非線性動力系統,被廣泛應用于模式識別、信號處理、自動控制、人工智能、聯想記憶等領域.而作為動力系統所表現出來的各種穩(wěn)態(tài)模式是神經網絡系統模擬生物神經系統學習、聯想、記憶及模式識別等一系列智能活動的基礎,在動力系統動態(tài)分析中,穩(wěn)定性是重要特性之一,因此研究時滯細胞神經網絡的各種穩(wěn)定性具有重要的理論和實踐意義.本文對幾類時滯細胞神經網絡的穩(wěn)定性進行了研究. 第一章首先介紹了神經網絡的發(fā)展及其應用前景.其次對時滯細胞神經網絡、隨機細胞神經網絡以及細胞神經網絡的同步性的研究現狀進行了簡單介紹. 第二章研究了變時滯隨機模糊細胞神經網絡的全局指數穩(wěn)定性,通過構造合適的Lyapunov泛函、利用Ito微分算子和不等式的分析技巧得到了該模型全局指數穩(wěn)定的一個時滯獨立和一個時滯依賴的充分條件. 第三章研究了帶馬爾可夫跳的時滯隨機細胞神經網絡的以分布漸近穩(wěn)定性.通過構造合適的Lyapunov泛函,得到了判定帶馬爾可夫跳的時滯隨機細胞神經網絡的以分布漸近穩(wěn)定的充分條件. 第四章研究了一類具比例時滯細胞神經網絡概周期的全局指數穩(wěn)定性,通過構造合適的Lyapunov泛函及一些不等式的分析,與Barbalat引理相結合,得到該網絡全局漸近穩(wěn)定性的充分條件. 第五章研究了一類變時滯細胞神經網絡平衡點的全局漸近同步性,通過構造合適的Lyapunov泛函及應用不等式的分析技巧,得到了具有驅動-響應結構的細胞神經網絡的全局漸近同步性的新的充分條件. 本文所得結論都是全新的,并且每一章都給出數值算例及其仿真結果,驗證了所得結論的有效性.
[Abstract]:Delayed cellular neural networks is a large-scale nonlinear dynamical system, is widely used in pattern recognition, signal processing, automatic control, artificial intelligence, associative memory and other fields. The steady-state model as a dynamic system is shown by neural network system simulation of biological neural system learning, Lenovo, a series of activities based intelligent memory and pattern recognition so, in the analysis of power system dynamic stability, is one of the important characteristics, has important theoretical and practical significance of various stability so the study of delayed cellular neural networks. The stability of several classes of neural networks with time delays is studied.
The first chapter introduces the development of neural network and its application prospect. The delayed cellular neural network, research status of the synchronization of stochastic cellular neural networks and cellular neural networks are introduced.
The second chapter studies the global exponential stability of stochastic fuzzy cellular neural networks with delays. By constructing suitable Lyapunov functional, using the analytical technique of Ito differential operators and inequalities obtained depends on the model for the global exponential stability of a delay independent and delay a sufficient condition.
The third chapter studies the stochastic cellular neural networks with Markovian jump to distribution asymptotic stability. By Lyapunov functional structure suitable, has been determined delay stochastic cellular neural networks with Markovian jump to full conditional distribution asymptotically stable.
The fourth chapter studies the global exponential stability of a class of cellular neural networks with proportional delays almost periodic, by constructing suitable Lyapunov functional analysis and some inequalities, combined with Barbalat's lemma, get the sufficient conditions for the global asymptotic stability of the network.
The fifth chapter studies a class of cellular neural networks with time varying delay equilibrium point of global asymptotic synchronization, through the analysis and application of Lyapunov technique to construct appropriate functional inequalities, obtained with the drive response of cellular neural network structure of the global asymptotic synchronization of the new sufficient conditions.
The conclusion of this paper is new, example and the simulation results and each chapter gives the numerical calculation, to verify the validity of the results.

【學位授予單位】：天津師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O175

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本文編號：1515740