具有时滞的复值神经网络稳定性分析
发布时间:2018-04-04 11:37
本文选题:复值神经网络 切入点:时滞 出处:《集美大学》2017年硕士论文
【摘要】:众所周知,时滞的存在可能导致神经网络系统不稳定,因而研究基于时滞的稳定性不仅具有理论价值也具有实际应用价值.同时由于复值神经网络比实值神经网络更具有一般性,能解决实值神经网络不能解决的问题.因此,具有时滞的复值神经网络稳定性成为了学者们研究的热点.基于前人的基础,我们将研究具有时滞的复值神经网络的稳定性并给出相关的稳定性判据.本文研究了具有时滞的复值神经网络的稳定性问题,主要内容包含三个方面:(1)研究了时标上具有时滞的复值递归神经网络全局指数稳定性.基于时标理论和压缩映射,不仅给出了解的存在唯一性条件且讨论了其指数稳定性.(2)研究了具有时滞的不连续复值神经网络的周期解的全局指数稳定性.运用Lyapunov稳定性方法,获得了周期解的一些准则并证明周期解的全局指数稳定性.(3)研究了具有比例时滞的复值神经网络的全局指数稳定性和周期性.利用Lyapunov稳定性方法,获得了该系统具有指数稳定性和周期性的新标准.
[Abstract]:It is well known that the existence of time delay may lead to the instability of neural network systems, so the study of the stability based on time delay has not only theoretical value but also practical application value.Because the complex neural network is more general than the real value neural network, it can solve the problems that can not be solved by the real value neural network.Therefore, the stability of complex valued neural networks with time delay has become a hot topic.Based on the previous results, we will study the stability of complex valued neural networks with time delay and give the relevant stability criteria.In this paper, the stability of complex valued neural networks with time delay is studied. The main contents include three aspects: 1) the global exponential stability of complex recurrent neural networks with time delays on time scales is studied.Based on time scale theory and contraction mapping, not only the existence and uniqueness conditions of solution are given, but also its exponential stability is discussed. (2) the global exponential stability of periodic solutions of discontinuous complex neural networks with time delay is studied.By using the Lyapunov stability method, some criteria of periodic solutions are obtained and the global exponential stability of periodic solutions is proved. 3) the global exponential stability and periodicity of complex neural networks with proportional delays are studied.A new criterion for exponential stability and periodicity of the system is obtained by using the Lyapunov stability method.
【学位授予单位】:集美大学
【学位级别】:硕士
【学位授予年份】:2017
【分类号】:O175
【参考文献】
相关期刊论文 前2条
1 闫欢;赵振江;宋乾坤;;具有泄漏时滞的复值神经网络的全局同步性[J];应用数学和力学;2016年08期
2 朱大奇;人工神经网络研究现状及其展望[J];江南大学学报;2004年01期
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