本文關鍵詞：離散耦合系統(tǒng)的穩(wěn)定條件分析及牽制控制同步　出處：《北京交通大學》2015年碩士論文　論文類型：學位論文

  更多相關文章： 同步 Rulkov模型 Hopfield網絡 牽制控制 小世界網絡

【摘要】：摘要：復雜網絡的穩(wěn)定性分析以及同步研究已經成為了當下的熱點之一,網絡連接結構也越來越多樣化,從規(guī)則網絡到完全隨機網絡,從小世界網絡到無尺度網絡,不同的耦合結構將使系統(tǒng)產生不同的行為,而對這些行為的研究分析可以被應用到包括生物、金融以及互聯(lián)網等領域中. 本文分為四個章節(jié), 第一章節(jié)介紹了相關的研究背景,包括Rulkov模型的研究發(fā)展進程,混沌的相關理論以及小世界網絡的構造原理等; 第二章節(jié)主要是多重時滯下離散環(huán)狀耦合系統(tǒng)的穩(wěn)定條件分析,首先研究了一個零分布特征多項式的性質,并將結果應用到神經網絡中,然后把理論從低維推廣到高維,從而得出了單個網絡和多個子網絡環(huán)狀耦合結構下的穩(wěn)定性條件,最后通過數(shù)值模擬驗證了結論; 第三章節(jié)則是利用牽制控制實現(xiàn)離散神經網絡的同步,具體方法就是在系統(tǒng)中加入自反饋控制項,利用李雅普諾夫函數(shù)法來證明其復雜系統(tǒng)的穩(wěn)定性,并且得到了其同步準則。最后我們利用在小世界網絡連接下的Rulkov模型驗證其同步準則. 第四章節(jié)是對全文的總結.
[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 .

【學位授予單位】：北京交通大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O157.5;O231

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