本文選題：復(fù)雜網(wǎng)絡(luò) + 網(wǎng)絡(luò)平均距離��； 參考：《廣西師范大學(xué)》2015年碩士論文

【摘要】：隨著人們生活日益的網(wǎng)絡(luò)化,復(fù)雜網(wǎng)絡(luò)已經(jīng)成為一個(gè)跨學(xué)科的新興領(lǐng)域,吸引了大量學(xué)者對(duì)其進(jìn)行研究。復(fù)雜網(wǎng)絡(luò)是對(duì)現(xiàn)實(shí)生活中各種復(fù)雜系統(tǒng)的描述,是通過(guò)把系統(tǒng)中的個(gè)體簡(jiǎn)化為節(jié)點(diǎn),個(gè)體間的相互關(guān)系用邊的連接來(lái)表示的方法獲得的。理解網(wǎng)絡(luò)結(jié)構(gòu)特征對(duì)網(wǎng)絡(luò)動(dòng)力學(xué)行為的影響,進(jìn)而對(duì)網(wǎng)絡(luò)行為進(jìn)行預(yù)測(cè)和改善是研究復(fù)雜網(wǎng)絡(luò)的主要目標(biāo)之一,復(fù)雜網(wǎng)絡(luò)上動(dòng)力系統(tǒng)的同步是其中的一項(xiàng)重要研究?jī)?nèi)容,具有重要的科學(xué)研究意義和實(shí)際應(yīng)用價(jià)值。在本論文,我們研究了網(wǎng)絡(luò)距離對(duì)同步能力的影響,探討了在群落網(wǎng)絡(luò)中網(wǎng)絡(luò)復(fù)雜度與單個(gè)群落的同步狀態(tài)隨群落間連邊數(shù)量的變化情況,分析了網(wǎng)絡(luò)距離與復(fù)雜度的關(guān)系,具體內(nèi)容如下：(1)網(wǎng)絡(luò)平均距離是重要的網(wǎng)絡(luò)結(jié)構(gòu)特征量,它對(duì)網(wǎng)絡(luò)同步能力有著重要的影響。以集聚系數(shù)和度分布保持不變的規(guī)則網(wǎng)絡(luò)模型為基礎(chǔ),通過(guò)數(shù)值模擬分析,我們發(fā)現(xiàn)無(wú)論網(wǎng)絡(luò)同步區(qū)域是有界的還是半無(wú)界的,網(wǎng)絡(luò)平均距離越小,網(wǎng)絡(luò)的同步能力越強(qiáng)。同時(shí),我們還考察了網(wǎng)絡(luò)節(jié)點(diǎn)間距離分布的異質(zhì)性對(duì)網(wǎng)絡(luò)同步能力的影響,給出了它們不同的數(shù)值關(guān)系。(2)對(duì)群落網(wǎng)絡(luò)中整個(gè)網(wǎng)絡(luò)復(fù)雜度與單個(gè)群落同步狀態(tài)進(jìn)行了比較。通過(guò)改變?nèi)郝溟g的連邊數(shù)量,分別在三種不同的情況下考察單個(gè)群落的同步狀態(tài)與網(wǎng)絡(luò)復(fù)雜度的變化情況：不同的振子作為網(wǎng)絡(luò)節(jié)點(diǎn)的動(dòng)力學(xué)系統(tǒng),不同的網(wǎng)絡(luò)耦合強(qiáng)度,不同的網(wǎng)絡(luò)平均度。通過(guò)數(shù)值模擬發(fā)現(xiàn)；網(wǎng)絡(luò)復(fù)雜度的極大值與單個(gè)群落同步狀態(tài)的極小值的位置非常接近,這表明在極值附近網(wǎng)絡(luò)處于在保持網(wǎng)絡(luò)整體信息通暢前提下實(shí)現(xiàn)的最大獨(dú)立程度的位置。(3)生活中常見(jiàn)的同步現(xiàn)象一般是處于部分同步狀態(tài),鑒于復(fù)雜度是研究網(wǎng)絡(luò)部分同步的重要參數(shù),我們研究了網(wǎng)絡(luò)平均距離對(duì)復(fù)雜度的影響。研究發(fā)現(xiàn)隨著平均距離的增加,復(fù)雜度都是先增加后減小的,表明在這一過(guò)程中網(wǎng)絡(luò)中先存在大的同步團(tuán)簇,之后大同步團(tuán)簇破裂成小的同步團(tuán)簇,平均距離的繼續(xù)增加導(dǎo)致小的同步團(tuán)簇也破碎掉。
[Abstract]:With the increasing network of people's life, complex network has become an interdisciplinary emerging field, attracting a large number of scholars to study it. Complex network is a description of various complex systems in real life. It is obtained by simplifying the individual in the system into nodes, and the relationship between individuals is represented by edge connection. It is one of the main goals of studying complex networks to understand the influence of network structure characteristics on network dynamic behavior, and then to predict and improve network behavior. Synchronization of dynamic systems on complex networks is one of the important research contents. It has important scientific research significance and practical application value. In this paper, we study the influence of network distance on synchronization ability, discuss the change of network complexity and synchronization status of a single community with the number of connected edges in a community network, and analyze the relationship between network distance and complexity. The main contents are as follows: (1) the average distance of network is an important characteristic quantity of network structure, which has an important influence on the network synchronization ability. Based on the regular network model with invariant agglomeration coefficient and degree distribution, we find that no matter whether the network synchronization region is bounded or semi-unbounded, the smaller the average distance of the network is, the stronger the synchronization capability of the network is. At the same time, we also investigate the influence of the heterogeneity of the distance distribution between the nodes on the synchronization ability of the network, and give their different numerical relationships. The complexity of the whole network in the community network is compared with the synchronization state of a single community. By changing the number of connected edges between communities, the changes of synchronization state and network complexity of a single community are investigated under three different conditions: different oscillators act as dynamic systems of network nodes, and different network coupling intensities. Different network averages. Through numerical simulation, it is found that the maximum of network complexity is very close to the minimum value of the synchronization state of a single community. This indicates that the network near the extremum is in the position of the maximum degree of independence realized under the premise of keeping the whole network information unobstructed.) the common synchronization phenomenon in life is generally in the state of partial synchronization. Since complexity is an important parameter in studying network partial synchronization, we study the influence of network average distance on complexity. It is found that with the increase of the average distance, the complexity increases first and then decreases, which indicates that in this process there are first large synchronous clusters, and then the large synchronous clusters break down into small synchronous clusters. The increasing of the average distance leads to the breakup of the small synchronous clusters.
【學(xué)位授予單位】：廣西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：O157.5

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