復雜動力網絡的拓撲識別：從單層到多層
發(fā)布時間：2018-09-08 15:21
【摘要】：網絡的拓撲結構表示其各個節(jié)點之間的相互連接關系,在決定網絡的演化機制和功能行為上起著重要作用,是分析預測和控制真實的復雜網絡動力學行為的前提條件.然而對于真實的復雜網絡而言,精確的拓撲結構往往是未知或者部分未知的,因此如何從已檢測到的節(jié)點動力學變量反演出網絡的拓撲結構就顯得尤為重要,這就是具有廣泛實際背景的復雜動力網絡的拓撲識別問題,也是復雜網絡科學發(fā)展研究中的一個具有挑戰(zhàn)性的問題.近幾年,復雜網絡拓撲識別逐漸引起了國內外許多學者的關注,對此展開了大量的研究工作,并在相對理想化的單層網絡拓撲結構識別問題上取得了較好的研究結果.本文主要對含有隨機擾動和耦合時滯的復雜網絡拓撲識別問題進行研究,并試圖將研究結果從單層網絡拓展到多層網絡.相比單層網絡而言,多層網絡更能模擬真實的網絡系統(tǒng),描述真正的網絡情景,因此隨著復雜網絡科學的發(fā)展,單層網絡已經不能滿足研究實際復雜系統(tǒng)的要求,而對多層網絡的研究和刻畫顯得迫切需要,這可以為探索大規(guī)模網絡的動力學演化機制及重塑網絡結構等問題奠定基礎,為信息、生物、社會等眾多學科的發(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狀,第2章給出與后續(xù)內容相關的基礎知識,第3到5章重點介紹本文所研究的相關工作,在此基礎上,第6章給出總結與對未來工作的展望.文章的主要內容和創(chuàng)新之處有如下幾點：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雜動力網絡的結構識別,將拓撲結構未知的原網絡看做驅動網絡,通過構造不含噪聲的響應網絡和設計合適的控制器,并結合隨機微分方程穩(wěn)定性理論來自適應地識別驅動網絡的拓撲結構.值得指出的是,所考慮的網絡模型含有隨機噪聲的擾動,但是為識別其結構而構造的網絡僅將驅動網絡的節(jié)點狀態(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絡隱藏源或者隱藏信息的探測,這也是一個新的發(fā)現,可以為工程實踐中網絡拓撲參數的追蹤和隱藏源的定位提供一定的理論指導和方法基礎.第4章在上一章基礎上給出基于廣義同步的網絡拓撲識別.本章通過自適應的控制技術使得未知結構網絡與構造的響應網絡達到廣義同步,并且原網絡未知的拓撲參數得以識別,而響應網絡的結構可以是已知的,未知的,甚至可以是不連通的孤立節(jié)點.值得指出的該方法不僅可以用于探測復雜系統(tǒng)的部分結構信息,以及對隱藏源的定位,而且在拓撲結構未知的網絡的節(jié)點動力學比較復雜或者維數較高時,輔助的響應網絡的結構卻可以非常簡單(表現在維數較低,節(jié)點動力學簡單等),這是一個前所未有的優(yōu)勢.第5章討論基于輔助系統(tǒng)法的雙層網絡識別.對于多層網絡我們往往只能獲得有限的節(jié)點信息或部分層的信息,因此這里所考慮的網絡是一個層間單向一一對應的雙層網絡,將輸出層看做驅動層,輸入層看做響應層,通過構造與響應層有相同結構的輔助層和設計簡單的自適應控制器來識別響應層的拓撲結構.該方法最大的特點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.仿真實驗驗證了理論結果的有效性,同時也得出了關于層間耦合強度變化時識別時間如何變化這一有意思的結論.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.
[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.
【學位授予單位】：武漢大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O157.5
[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.
【學位授予單位】：武漢大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O157.5
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