本文關(guān)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(xué)》2015年碩士論文　論文類(lèi)型：學(xué)位論文

  更多相關(guān)文章： 同步 Rulkov模型 Hopfield網(wǎng)絡(luò) 牽制控制 小世界網(wǎng)絡(luò)

【摘要】：摘要：復(fù)雜網(wǎng)絡(luò)的穩(wěn)定性分析以及同步研究已經(jīng)成為了當(dāng)下的熱點(diǎn)之一,網(wǎng)絡(luò)連接結(jié)構(gòu)也越來(lái)越多樣化,從規(guī)則網(wǎng)絡(luò)到完全隨機(jī)網(wǎng)絡(luò),從小世界網(wǎng)絡(luò)到無(wú)尺度網(wǎng)絡(luò),不同的耦合結(jié)構(gòu)將使系統(tǒng)產(chǎn)生不同的行為,而對(duì)這些行為的研究分析可以被應(yīng)用到包括生物、金融以及互聯(lián)網(wǎng)等領(lǐng)域中. 本文分為四個(gè)章節(jié), 第一章節(jié)介紹了相關(guān)的研究背景,包括Rulkov模型的研究發(fā)展進(jìn)程,混沌的相關(guān)理論以及小世界網(wǎng)絡(luò)的構(gòu)造原理等; 第二章節(jié)主要是多重時(shí)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(gè)零分布特征多項(xiàng)式的性質(zhì),并將結(jié)果應(yīng)用到神經(jīng)網(wǎng)絡(luò)中,然后把理論從低維推廣到高維,從而得出了單個(gè)網(wǎng)絡(luò)和多個(gè)子網(wǎng)絡(luò)環(huán)狀耦合結(jié)構(gòu)下的穩(wěn)定性條件,最后通過(guò)數(shù)值模擬驗(yàn)證了結(jié)論; 第三章節(jié)則是利用牽制控制實(shí)現(xiàn)離散神經(jīng)網(wǎng)絡(luò)的同步,具體方法就是在系統(tǒng)中加入自反饋控制項(xiàng),利用李雅普諾夫函數(shù)法來(lái)證明其復(fù)雜系統(tǒng)的穩(wěn)定性,并且得到了其同步準(zhǔn)則。最后我們利用在小世界網(wǎng)絡(luò)連接下的Rulkov模型驗(yàn)證其同步準(zhǔn)則. 第四章節(jié)是對(duì)全文的總結(jié).
[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(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：O157.5;O231

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本文編號(hào)：1391247