【摘要】：網(wǎng)絡(luò)的拓?fù)浣Y(jié)構(gòu)表示其各個節(jié)點(diǎn)之間的相互連接關(guān)系,在決定網(wǎng)絡(luò)的演化機(jī)制和功能行為上起著重要作用,是分析預(yù)測和控制真實(shí)的復(fù)雜網(wǎng)絡(luò)動力學(xué)行為的前提條件.然而對于真實(shí)的復(fù)雜網(wǎng)絡(luò)而言,精確的拓?fù)浣Y(jié)構(gòu)往往是未知或者部分未知的,因此如何從已檢測到的節(jié)點(diǎn)動力學(xué)變量反演出網(wǎng)絡(luò)的拓?fù)浣Y(jié)構(gòu)就顯得尤為重要,這就是具有廣泛實(shí)際背景的復(fù)雜動力網(wǎng)絡(luò)的拓?fù)渥R別問題,也是復(fù)雜網(wǎng)絡(luò)科學(xué)發(fā)展研究中的一個具有挑戰(zhàn)性的問題.近幾年,復(fù)雜網(wǎng)絡(luò)拓?fù)渥R別逐漸引起了國內(nèi)外許多學(xué)者的關(guān)注,對此展開了大量的研究工作,并在相對理想化的單層網(wǎng)絡(luò)拓?fù)浣Y(jié)構(gòu)識別問題上取得了較好的研究結(jié)果.本文主要對含有隨機(jī)擾動和耦合時滯的復(fù)雜網(wǎng)絡(luò)拓?fù)渥R別問題進(jìn)行研究,并試圖將研究結(jié)果從單層網(wǎng)絡(luò)拓展到多層網(wǎng)絡(luò).相比單層網(wǎng)絡(luò)而言,多層網(wǎng)絡(luò)更能模擬真實(shí)的網(wǎng)絡(luò)系統(tǒng),描述真正的網(wǎng)絡(luò)情景,因此隨著復(fù)雜網(wǎng)絡(luò)科學(xué)的發(fā)展,單層網(wǎng)絡(luò)已經(jīng)不能滿足研究實(shí)際復(fù)雜系統(tǒng)的要求,而對多層網(wǎng)絡(luò)的研究和刻畫顯得迫切需要,這可以為探索大規(guī)模網(wǎng)絡(luò)的動力學(xué)演化機(jī)制及重塑網(wǎng)絡(luò)結(jié)構(gòu)等問題奠定基礎(chǔ),為信息、生物、社會等眾多學(xué)科的發(fā)展和研究提供新的視角和方法.文章一共分為6章,第1章簡要介紹本文的研究背景和研究現(xiàn)狀,第2章給出與后續(xù)內(nèi)容相關(guān)的基礎(chǔ)知識,第3到5章重點(diǎn)介紹本文所研究的相關(guān)工作,在此基礎(chǔ)上,第6章給出總結(jié)與對未來工作的展望.文章的主要內(nèi)容和創(chuàng)新之處有如下幾點(diǎn)：第3章首先研究基于完全同步的噪聲擾動下的單層時滯復(fù)雜動力網(wǎng)絡(luò)的結(jié)構(gòu)識別,將拓?fù)浣Y(jié)構(gòu)未知的原網(wǎng)絡(luò)看做驅(qū)動網(wǎng)絡(luò),通過構(gòu)造不含噪聲的響應(yīng)網(wǎng)絡(luò)和設(shè)計合適的控制器,并結(jié)合隨機(jī)微分方程穩(wěn)定性理論來自適應(yīng)地識別驅(qū)動網(wǎng)絡(luò)的拓?fù)浣Y(jié)構(gòu).值得指出的是,所考慮的網(wǎng)絡(luò)模型含有隨機(jī)噪聲的擾動,但是為識別其結(jié)構(gòu)而構(gòu)造的網(wǎng)絡(luò)僅將驅(qū)動網(wǎng)絡(luò)的節(jié)點(diǎn)狀態(tài)作為控制輸入而不含噪聲,這在一定程度上大大簡化了識別程序,從而提高識別效率.此外,所提出的控制方法可以有效的用于網(wǎng)絡(luò)隱藏源或者隱藏信息的探測,這也是一個新的發(fā)現(xiàn),可以為工程實(shí)踐中網(wǎng)絡(luò)拓?fù)鋮?shù)的追蹤和隱藏源的定位提供一定的理論指導(dǎo)和方法基礎(chǔ).第4章在上一章基礎(chǔ)上給出基于廣義同步的網(wǎng)絡(luò)拓?fù)渥R別.本章通過自適應(yīng)的控制技術(shù)使得未知結(jié)構(gòu)網(wǎng)絡(luò)與構(gòu)造的響應(yīng)網(wǎng)絡(luò)達(dá)到廣義同步,并且原網(wǎng)絡(luò)未知的拓?fù)鋮?shù)得以識別,而響應(yīng)網(wǎng)絡(luò)的結(jié)構(gòu)可以是已知的,未知的,甚至可以是不連通的孤立節(jié)點(diǎn).值得指出的該方法不僅可以用于探測復(fù)雜系統(tǒng)的部分結(jié)構(gòu)信息,以及對隱藏源的定位,而且在拓?fù)浣Y(jié)構(gòu)未知的網(wǎng)絡(luò)的節(jié)點(diǎn)動力學(xué)比較復(fù)雜或者維數(shù)較高時,輔助的響應(yīng)網(wǎng)絡(luò)的結(jié)構(gòu)卻可以非常簡單(表現(xiàn)在維數(shù)較低,節(jié)點(diǎn)動力學(xué)簡單等),這是一個前所未有的優(yōu)勢.第5章討論基于輔助系統(tǒng)法的雙層網(wǎng)絡(luò)識別.對于多層網(wǎng)絡(luò)我們往往只能獲得有限的節(jié)點(diǎn)信息或部分層的信息,因此這里所考慮的網(wǎng)絡(luò)是一個層間單向一一對應(yīng)的雙層網(wǎng)絡(luò),將輸出層看做驅(qū)動層,輸入層看做響應(yīng)層,通過構(gòu)造與響應(yīng)層有相同結(jié)構(gòu)的輔助層和設(shè)計簡單的自適應(yīng)控制器來識別響應(yīng)層的拓?fù)浣Y(jié)構(gòu).該方法最大的特點(diǎn)就是控制器比較簡單,可以大大縮減控制輸入信息量,提高控制識別效率.仿真實(shí)驗(yàn)驗(yàn)證了理論結(jié)果的有效性,同時也得出了關(guān)于層間耦合強(qiáng)度變化時識別時間如何變化這一有意思的結(jié)論.希望能為謠言傳播,偽信息傳播的路線和源頭定位提供一定的理論基礎(chǔ).
[Abstract]:The topological structure of a network represents the interconnection between its nodes and plays an important role in determining the evolution mechanism and functional behavior of the network. It is a prerequisite for analyzing, predicting and controlling the dynamic behavior of a real complex network. In recent years, topology identification of complex dynamical networks is a challenging problem in the scientific development of complex networks. Many scholars at home and abroad pay more and more attention to this problem, and a lot of research work has been carried out, and good results have been obtained on the problem of identifying the topological structure of relatively ideal single-layer networks. Single-layer network extends to multi-layer network. Compared with single-layer network, multi-layer network can better simulate the real network system and describe the real network scenario. Therefore, with the development of complex network science, single-layer network can no longer meet the requirements of researching the actual complex system, and it is urgent to study and characterize multi-layer network. In order to lay a foundation for exploring the dynamic evolution mechanism of large-scale networks and reshaping the network structure, and to provide a new perspective and method for the development and research of information, biology, society and many other disciplines, this paper is divided into six chapters. Chapter 1 briefly introduces the research background and current situation of this paper. Chapter 2 gives the basis related to the follow-up content. Chapters 3 to 5 focus on the related work of this paper, and on this basis, Chapter 6 gives a summary and outlook for future work. The main contents and innovations of this paper are as follows: Chapter 3 first studies the structure identification of single-layer complex dynamic networks with time-delay based on completely synchronous noise disturbances, and the topological junction is proposed. The original network with unknown structure is regarded as a driving network. The topology of the driving network can be adaptively identified by constructing a response network without noise and designing an appropriate controller. It is worth pointing out that the network model considered contains disturbances of random noise but is structured to identify its structure. In addition, the proposed control method can be effectively used to detect hidden sources or hidden information in the network, which is also a new discovery and can be used in engineering practice. Chapter 4 gives the topology identification based on generalized synchronization. In this chapter, adaptive control technology is used to make the unknown network and the constructed response network achieve generalized synchronization, and the original network is unknown. The structure of the response network can be known, unknown, or even disconnected isolated nodes. It is worth pointing out that this method can be used not only to detect some structural information of complex systems, but also to locate hidden sources. Moreover, the node dynamics of the network with unknown topological structure is complex or even unconnected. Chapter 5 discusses two-layer network identification based on auxiliary system method. For multi-layer networks, we can only obtain limited node information or part of the layer information, therefore, we can only obtain limited node information. The network considered here is a two-layer network with one-to-one correspondence between layers. The output layer is regarded as the driving layer, the input layer as the response layer, and the topology of the response layer is identified by constructing an auxiliary layer with the same structure as the response layer and designing a simple adaptive controller. The simulation results show the effectiveness of the theoretical results and the interesting conclusion about how to change the identification time when the coupling strength between layers changes. It is hoped that this paper can provide a theoretical basis for rumor propagation, the route of false information propagation and the source location. Foundation.
【學(xué)位授予單位】：武漢大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O157.5

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