【摘要】：隨著全球經(jīng)濟一體化,科學技術(shù)的飛速發(fā)展,許許多多產(chǎn)品的完成、產(chǎn)業(yè)的發(fā)展都需要國與國之間,產(chǎn)業(yè)與產(chǎn)業(yè)之間,不同技術(shù)層面的人與人之間的緊密合作來完成,如航天、高鐵、人類基因組計劃等的實現(xiàn)。然而,不同的行業(yè)之間的這種合作應(yīng)該怎么去進行,主行業(yè)公司尋找優(yōu)秀的子行業(yè)公司合作,子行業(yè)公司又尋找優(yōu)秀的子子行業(yè)公司合作,這樣擇優(yōu)下去就形成了一個龐大的社會行業(yè)擇優(yōu)網(wǎng)。因此,研究這樣的網(wǎng)絡(luò)怎樣演化,演化后的結(jié)構(gòu)又有什么樣的特性對產(chǎn)業(yè)間的合作有很大的意義�；诖�,本文拓展了BA無標度網(wǎng)絡(luò)模型,考慮在一次擇優(yōu)連接后,根據(jù)節(jié)點的屬性要求自動發(fā)出邊進行第二次連續(xù)擇優(yōu)連接,甚至第三次擇優(yōu)連接,給網(wǎng)絡(luò)結(jié)構(gòu)帶來的影響。第一章,概述研究網(wǎng)絡(luò)生成模型的意義、反映網(wǎng)絡(luò)拓撲結(jié)構(gòu)的數(shù)學特性、經(jīng)典的生成網(wǎng)絡(luò)模型以及介紹本文的研究成果。第二章,基于原始BA網(wǎng)絡(luò)模型,重點研究新節(jié)點進入網(wǎng)絡(luò)發(fā)出一次優(yōu)先連接后,被選中連邊的節(jié)點會根據(jù)新節(jié)點的需求自動發(fā)出邊再一次優(yōu)先連接網(wǎng)絡(luò)中另外的節(jié)點的網(wǎng)絡(luò)演化情形。進而,利用平均場的方法對該模型進行理論分析,得到了該模型的度及其度分布,之后通過隨機模擬和數(shù)值模擬的對比,對比結(jié)果完全的體現(xiàn)出了無標度網(wǎng)絡(luò)的特性,其度分布情況與冪律分布一致。第三章,在第二章的基礎(chǔ)上考慮三次連續(xù)優(yōu)先連接的情形,同樣應(yīng)用平均場的方法對模型進行理論分析,得到模型的節(jié)點度及其度分布;進而,隨機模擬和數(shù)值模擬對比的一致性不僅驗證了理論分析,并且表明冪指數(shù)的可調(diào)范圍變大,增進了我們對實際網(wǎng)絡(luò)的進一步了解。
[Abstract]:With the globalization of the global economy, the rapid development of science and technology, the completion of many products, the development of industry needs close cooperation between countries, industries and industries, and between people at different technical levels, such as spaceflight. High Speed, the realization of the Human Genome Project. However, how should this kind of cooperation be carried out between different industries? the main industry company is looking for excellent sub-industry companies, and sub-industry companies are looking for excellent sub-industry companies to cooperate. In this way, the selection of the best to form a huge network of social industries. Therefore, it is of great significance to study how the network evolves and what the characteristics of the evolving structure are for the cooperation between industries. Based on this, this paper extends the scale-free network model of BA, and considers the influence of the second continuous optimal connection, even the third optimal connection, on the network structure after the first selective connection, according to the attribute requirement of the node. In the first chapter, the significance of the research on the network generation model, the mathematical characteristics of the network topology, the classical generation network model and the research results of this paper are summarized. The second chapter, based on the original BA network model, focuses on the priority connection after the new node enters the network. The selected connected nodes automatically send out the network evolution of the other nodes in the network according to the requirements of the new node. Furthermore, the degree and degree distribution of the model are obtained through the theoretical analysis of the model by means of the mean field method, and the comparison between the random simulation and the numerical simulation shows the characteristics of the scale-free network completely. The degree distribution is consistent with the power law distribution. In the third chapter, considering the case of three consecutive priority connections on the basis of the second chapter, the model is theoretically analyzed by the method of mean field, and the node degree and its degree distribution of the model are obtained. Furthermore, the consistency between stochastic simulation and numerical simulation not only verifies the theoretical analysis, but also shows that the adjustable range of power exponents is becoming larger, which enhances our further understanding of the actual network.
【學位授予單位】：中北大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：O157.5

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