离散耦合系统的稳定条件分析及牵制控制同步

发布时间：2018-01-07 05:47

本文关键词：离散耦合系统的稳定条件分析及牵制控制同步　出处：《北京交通大学》2015年硕士论文　论文类型：学位论文

【摘要】：摘要：复杂网络的稳定性分析以及同步研究已经成为了当下的热点之一,网络连接结构也越来越多样化,从规则网络到完全随机网络,从小世界网络到无尺度网络,不同的耦合结构将使系统产生不同的行为,而对这些行为的研究分析可以被应用到包括生物、金融以及互联网等领域中. 本文分为四个章节, 第一章节介绍了相关的研究背景,包括Rulkov模型的研究发展进程,混沌的相关理论以及小世界网络的构造原理等; 第二章节主要是多重时滞下离散环状耦合系统的稳定条件分析,首先研究了一个零分布特征多项式的性质,并将结果应用到神经网络中,然后把理论从低维推广到高维,从而得出了单个网络和多个子网络环状耦合结构下的稳定性条件,最后通过数值模拟验证了结论; 第三章节则是利用牵制控制实现离散神经网络的同步,具体方法就是在系统中加入自反馈控制项,利用李雅普诺夫函数法来证明其复杂系统的稳定性,并且得到了其同步准则。最后我们利用在小世界网络连接下的Rulkov模型验证其同步准则. 第四章节是对全文的总结.
[Abstract]:Abstract : The stability analysis and synchronization of complex networks have become one of the hot topics in the present . The network connection structure has become more and more diversified . From the regular network to the complete random network , from the small world network to the non - scale network , different coupling structures will lead to different behaviors of the system , and the research and analysis of these behaviors can be applied to the fields including biology , finance and the Internet . This article is divided into four chapters . The first chapter introduces the relevant research background , including the research development process , the theory of chaos and the construction principle of the small world network . The second chapter is mainly the stability condition analysis of the discrete loop coupling system with multiple time lag . First , the property of a zero distribution characteristic polynomial is studied , and the result is applied to the neural network , then the theory is extended from the low dimension to the high dimension , so that the stability conditions under the ring - coupled structure of a single network and a plurality of sub - networks are obtained , and finally the conclusion is verified by numerical simulation ; In chapter 3 , the synchronization of discrete neural networks is realized by using the control method . The method is to add the self - feedback control term to the system , and the Lyapunov function method is used to prove the stability of the complex system , and the synchronization criterion is obtained . Section IV is a summary of the full text .

【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5;O231

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