本文選題：復雜網(wǎng)絡 + 級聯(lián)失效　； 參考：《天津理工大學》2017年碩士論文

【摘要】：信息時代的腳步聲越來越近,復雜網(wǎng)絡學科的引入為更加深入地研究復雜系統(tǒng)的結構特征與其上的動力學行為提供了詳細的理論基礎和方法。本論文涉及的研究工作主要與復雜網(wǎng)絡系統(tǒng)的模型實現(xiàn)與特性分析相關:基于耦合網(wǎng)絡攻擊問題的研究,有助于增強對現(xiàn)實生活中復雜相依系統(tǒng)的理解和認知;采用數(shù)值仿真的方法分析了復雜網(wǎng)絡的結構可控能力,研究結果有助于探尋提升網(wǎng)絡系統(tǒng)可控能力的關鍵因素;基于Fitness模型對冪指數(shù)可變的無標度網(wǎng)絡進行建模實現(xiàn),并進一步深入分析其重要的結構特征及動力學特性,研究結果有力證明了冪指數(shù)γ對無標度網(wǎng)絡性能的重要影響。論文的主要研究內(nèi)容和創(chuàng)新性成果概括如下:1.攻擊引發(fā)的相依網(wǎng)絡系統(tǒng)中級聯(lián)失效行為分析。針對蓄意攻擊引發(fā)的相依系統(tǒng)級聯(lián)失效行為,進一步驗證耦合關系對相依系統(tǒng)抗攻擊能力的影響,引入相依網(wǎng)絡系統(tǒng)模型,通過控制該網(wǎng)絡模型的兩個調(diào)優(yōu)參數(shù),深入分析度分布,尤其是度異質(zhì)程度的變化規(guī)律。以數(shù)值模擬手段,討論和驗證度分布異質(zhì)程度對單網(wǎng)絡和相依網(wǎng)絡結構脆弱性的影響,著重分析網(wǎng)絡耦合強度對蓄意攻擊情況下的相依網(wǎng)絡系統(tǒng)的作用,研究結果有助于進一步深刻理解現(xiàn)實世界中多網(wǎng)絡系統(tǒng)的結構脆弱性特征。2.Local-World網(wǎng)絡的結構可控性研究。Local-World網(wǎng)絡模型已經(jīng)成為一個成熟的網(wǎng)絡模型框架,對其進行網(wǎng)絡可控性研究有著重要的意義。以控制信號的可達性為基礎,借助仿真手段,研究了Local-World網(wǎng)絡中影響結構可控性的關鍵因素。結果表明,對于密集網(wǎng)絡,可控性取決于網(wǎng)絡規(guī)模N,Local-World效應暫時可忽略不計;對于稀疏網(wǎng)絡,與網(wǎng)絡規(guī)模N相比,局部網(wǎng)絡規(guī)模M更能顯著地影響結構可控能力。3.冪指數(shù)可變的無標度網(wǎng)絡的建模與分析。度分布服從冪律的網(wǎng)絡被稱為無標度網(wǎng)絡,Fitness模型作為典型無標度模型之一,能生成度分布冪指數(shù)可變的無標度網(wǎng)絡,其冪指數(shù)γ的取值范圍為γ∈(2,∞)。在簡介Fitness網(wǎng)絡建模機理的基礎上,給出了模型的具體實現(xiàn)方法,并針對所生成的網(wǎng)絡,進一步對其重要的結構特征及動力學特性進行了深入分析,包括度分布、抗攻擊能力、同步性能及結構可控能力,重點研究了冪指數(shù)γ對網(wǎng)絡性能的影響。
[Abstract]:The step sound of the information age is getting closer and closer. The introduction of the complex network provides a detailed theoretical basis and method for the further study of the structural characteristics and the dynamic behavior of the complex system. The research work in this thesis is mainly related to the model realization of complex network system and characteristic analysis. The research based on coupling network attack can help to enhance the understanding and cognition of complex dependent system in real life. The structural controllability of complex networks is analyzed by numerical simulation, and the results are helpful to explore the key factors to improve the controllability of network systems. Based on the Fitness model, the scale-free networks with variable power exponents are modeled and implemented. Furthermore, the important structural and dynamic characteristics are analyzed. The results show that the power exponent 緯 has an important effect on the performance of scale-free networks. The main research contents and innovative results are summarized as follows: 1. Analysis of cascading failure behavior in dependent Network system caused by attack. Aiming at the cascade failure behavior of dependent system caused by intentional attack, this paper further verifies the effect of coupling relation on the anti-attack ability of dependent system, introduces the dependent network system model, and controls the two tuning parameters of the network model. The variation of degree distribution, especially degree heterogeneity, is deeply analyzed. By means of numerical simulation, the influence of degree distribution heterogeneity on the vulnerability of single network and dependent network structure is discussed and verified, and the effect of network coupling strength on dependent network system under intentional attack is analyzed. The results of the study are helpful to further understand the structural vulnerability characteristics of multi-network systems in the real world. 2. The structural controllability of Local-World networks; the Local-World network model has become a mature network model framework. It is of great significance to study the network controllability. Based on the reachability of control signal, the key factors influencing the controllability of Local-World network are studied by means of simulation. The results show that, for dense networks, controllability depends on the network size, which is negligible for the time being, and for sparse networks, the local network size M can significantly affect the controllability of the structure compared with the network size N. Modeling and analysis of scale-free networks with variable power exponents. The scale-free network Fitness model is one of the typical scale-free models. It can generate scale-free networks with variable power exponent. The range of power exponent 緯 is 緯 鈭，

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