本文選題：和諧統(tǒng)一混合擇優(yōu)網(wǎng)絡(luò) + κ均勻無標(biāo)度超網(wǎng)絡(luò)�。� 參考：《陜西師范大學(xué)》2016年博士論文

【摘要】：隨著當(dāng)代科學(xué)技術(shù)的不斷發(fā)展,網(wǎng)絡(luò)充滿了人類社會(huì)的各個(gè)領(lǐng)域,并日益影響著人們的生產(chǎn)和生活.對(duì)各種復(fù)雜網(wǎng)絡(luò)建模和拓?fù)湫再|(zhì)的分析使人們對(duì)復(fù)雜網(wǎng)絡(luò)有了深入的了解,而復(fù)雜網(wǎng)絡(luò)動(dòng)力學(xué)性質(zhì)的研究是復(fù)雜網(wǎng)絡(luò)研究的終極目標(biāo)之一,對(duì)網(wǎng)絡(luò)動(dòng)力學(xué)性質(zhì)的研究可以幫助人們更清楚的認(rèn)識(shí)網(wǎng)絡(luò)的特性,解決很多實(shí)際問題.例如北美大停電事故體現(xiàn)了網(wǎng)絡(luò)的相繼故障行為,而復(fù)雜系統(tǒng)的信號(hào)輸入問題又可以用網(wǎng)絡(luò)的可控性來解決等.目前對(duì)網(wǎng)絡(luò)相繼故障、同步、控制和傳播等動(dòng)力學(xué)性質(zhì)的研究已成為網(wǎng)絡(luò)科學(xué)研究的主題和熱點(diǎn).本文基于復(fù)雜網(wǎng)絡(luò)理論、超圖和超網(wǎng)絡(luò)理論等多學(xué)科領(lǐng)域的知識(shí)和方法,研究了一類和諧統(tǒng)一混合擇優(yōu)網(wǎng)絡(luò)的相繼故障行為.針對(duì)現(xiàn)實(shí)超網(wǎng)絡(luò)相繼故障的特點(diǎn)研究κ均勻無標(biāo)度超網(wǎng)絡(luò)的相繼故障行為.討論了度序列相同的一類確定性網(wǎng)絡(luò)的可控性,并提出了一類確定性超網(wǎng)絡(luò)的構(gòu)建方法,探討了這類確定性超網(wǎng)絡(luò)的可控性.主要內(nèi)容如下:(1)分析了一類和諧統(tǒng)一混合擇優(yōu)網(wǎng)絡(luò)耦合映像格子的相繼故障行為,獲得了該網(wǎng)絡(luò)抵抗隨機(jī)攻擊和蓄意攻擊的能力,發(fā)現(xiàn)了測(cè)量該網(wǎng)絡(luò)魯棒性的測(cè)度.另外,理論推導(dǎo)了使網(wǎng)絡(luò)達(dá)到全局崩潰所需的擾動(dòng)閾值的近似值,并和實(shí)驗(yàn)結(jié)果進(jìn)行了對(duì)比,驗(yàn)證了理論分析的有效性.(2)針對(duì)現(xiàn)實(shí)中的快遞超網(wǎng)絡(luò)和電子元件超網(wǎng)絡(luò)上相繼故障的擴(kuò)散特點(diǎn),利用超圖理論,首次提出了分析這兩類超網(wǎng)絡(luò)相繼故障行為的方法.并分析了 均勻無標(biāo)度超網(wǎng)絡(luò)耦合映像格子的相繼故障行為及這類超網(wǎng)絡(luò)遭受隨機(jī)攻擊和蓄意攻擊時(shí)的魯棒性及影響超網(wǎng)絡(luò)魯棒性的因素,并與普通網(wǎng)絡(luò)的魯棒性進(jìn)行了對(duì)比.同時(shí)給出了 κκ均勻無標(biāo)度超網(wǎng)絡(luò)擾動(dòng)閾值的理論近似值,并和實(shí)驗(yàn)結(jié)果進(jìn)行了比較.(3)基于超網(wǎng)絡(luò)的超鄰接矩陣和聯(lián)合度首次提出了一種適合描述超網(wǎng)絡(luò)相繼故障行為的新模型,并利用該模型仿真模擬了 3均勻無標(biāo)度超網(wǎng)絡(luò)的相繼故障行為,分析了該超網(wǎng)絡(luò)的魯棒性及其影響因素.明確了3均勻無標(biāo)度超網(wǎng)絡(luò)擾動(dòng)閾值的理論近似值,通過和實(shí)驗(yàn)數(shù)據(jù)的對(duì)比驗(yàn)證了理論分析的有效性.(4)利用精確可控性理論,分析了一類度序列相同的確定性(x,y)-花網(wǎng)絡(luò)的可控性,給出了這類網(wǎng)絡(luò)的最小驅(qū)動(dòng)節(jié)點(diǎn)集的精確解;同時(shí),通過對(duì)(x,y)-花網(wǎng)絡(luò)進(jìn)行擴(kuò)展,首次提出了一類確定性2κ均勻超(1,3)-花網(wǎng)絡(luò)的構(gòu)建算法,結(jié)合超圖理論和精確可控性理論,首次分析了這類確定性超網(wǎng)絡(luò)的可控性.
[Abstract]:With the continuous development of modern science and technology, the network is full of various fields of human society, and increasingly affects people's production and life.The modeling and topology analysis of various complex networks make people have a deep understanding of complex networks, and the study of dynamic properties of complex networks is one of the ultimate goals of the study of complex networks.The study of network dynamics can help people to understand the characteristics of the network more clearly and solve many practical problems.For example, the blackout in North America reflects the successive fault behavior of the network, and the signal input problem of the complex system can be solved by the controllability of the network.At present, the research on the dynamic properties of network failure, synchronization, control and propagation has become the topic and hotspot of network science.Based on the knowledge and methods of complex network theory, hypergraph and supernetwork theory, the sequential fault behavior of a class of harmonious and unified hybrid optimal networks is studied in this paper.The sequential fault behavior of 魏 uniform scale-free supernetwork is studied according to the characteristics of sequential faults in real supernetworks.The controllability of a class of deterministic networks with the same degree sequence is discussed, and the construction method of a class of deterministic supernetworks is proposed, and the controllability of this kind of deterministic supernetworks is discussed.The main contents are as follows: 1) in this paper, the successive fault behavior of a class of harmonious and unified hybrid optimal network coupled map lattice is analyzed. The capability of resisting random and deliberate attacks is obtained, and the measure of robustness of the network is found.In addition, the approximate perturbation threshold for global collapse of the network is derived and compared with the experimental results.The validity of theoretical analysis is verified. (2) aiming at the diffusion characteristics of successive faults in express delivery supernetwork and electronic component supernetwork, a method to analyze the sequential fault behavior of these two supernetworks is proposed for the first time by using hypergraph theory.The sequential failure behavior of coupled mapping lattice of uniform scale-free supernetwork, the robustness of this kind of supernetwork under random and deliberate attack and the factors influencing the robustness of supernetwork are analyzed, and compared with that of ordinary network.At the same time, the theoretical approximation of the perturbation threshold of 魏 -uniform scale-free supernetwork is given.Compared with the experimental results, a new model is proposed for the first time based on the superadjacent matrix and the degree of association of the supernetwork, which is suitable for describing the sequential fault behavior of the supernetwork.The model is used to simulate the sequential fault behavior of 3 uniform scale-free supernetwork, and the robustness of the supernetwork and its influencing factors are analyzed.The theoretical approximation of perturbation threshold of 3 uniform scale-free supernetwork is defined. The validity of theoretical analysis is verified by comparing with experimental data.In this paper, the controllability of a class of deterministic networks with the same degree sequence is analyzed, and the exact solution of the minimum driving node set of the networks is given.For the first time, a class of deterministic 2 魏 uniform supernetwork is proposed. The controllability of this kind of deterministic supernetwork is analyzed for the first time by combining the theory of hypergraph with the theory of precise controllability.
【學(xué)位授予單位】：陜西師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O157.5

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本文編號(hào)：1771725