时滞细胞神经网络的全局稳定性与同步性

发布时间：2018-02-16 14:32

本文关键词： 时滞细胞神经网络指数稳定性渐近稳定性以分布渐近稳定性渐近同步性 Lyapunov泛函　出处：《天津师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：时滞细胞神经网络是一大规模非线性动力系统,被广泛应用于模式识别、信号处理、自动控制、人工智能、联想记忆等领域.而作为动力系统所表现出来的各种稳态模式是神经网络系统模拟生物神经系统学习、联想、记忆及模式识别等一系列智能活动的基础,在动力系统动态分析中,稳定性是重要特性之一,因此研究时滞细胞神经网络的各种稳定性具有重要的理论和实践意义.本文对几类时滞细胞神经网络的稳定性进行了研究. 第一章首先介绍了神经网络的发展及其应用前景.其次对时滞细胞神经网络、随机细胞神经网络以及细胞神经网络的同步性的研究现状进行了简单介绍. 第二章研究了变时滞随机模糊细胞神经网络的全局指数稳定性,通过构造合适的Lyapunov泛函、利用Ito微分算子和不等式的分析技巧得到了该模型全局指数稳定的一个时滞独立和一个时滞依赖的充分条件. 第三章研究了带马尔可夫跳的时滞随机细胞神经网络的以分布渐近稳定性.通过构造合适的Lyapunov泛函,得到了判定带马尔可夫跳的时滞随机细胞神经网络的以分布渐近稳定的充分条件. 第四章研究了一类具比例时滞细胞神经网络概周期的全局指数稳定性,通过构造合适的Lyapunov泛函及一些不等式的分析,与Barbalat引理相结合,得到该网络全局渐近稳定性的充分条件. 第五章研究了一类变时滞细胞神经网络平衡点的全局渐近同步性,通过构造合适的Lyapunov泛函及应用不等式的分析技巧,得到了具有驱动-响应结构的细胞神经网络的全局渐近同步性的新的充分条件. 本文所得结论都是全新的,并且每一章都给出数值算例及其仿真结果,验证了所得结论的有效性.
[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.

【学位授予单位】：天津师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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