本文選題：復(fù)雜網(wǎng)絡(luò) + 非線性動(dòng)力學(xué)��； 參考：《華東師范大學(xué)》2016年博士論文

【摘要】：爆炸式同步(explosive synchronization)現(xiàn)象指的是復(fù)雜網(wǎng)絡(luò)從混亂狀態(tài)變化到同步狀態(tài)的過(guò)程是一個(gè)不連續(xù)的、伴隨著磁滯現(xiàn)象的一級(jí)相變過(guò)程,這與人們所熟知的同步相變多為連續(xù)的、無(wú)磁滯的二級(jí)相變的結(jié)論截然不同。在爆炸式同步現(xiàn)象中,系統(tǒng)具有兩個(gè)穩(wěn)態(tài)并且在兩個(gè)穩(wěn)態(tài)間的切換是快速,不連續(xù)的,這與現(xiàn)實(shí)中的很多突發(fā)性現(xiàn)象如大腦中的癲癇病爆發(fā)以及電網(wǎng)中的級(jí)聯(lián)失效等有高度相似性。由于2009年以來(lái)爆炸式滲流問(wèn)題在復(fù)雜網(wǎng)絡(luò)領(lǐng)域的火熱,復(fù)雜網(wǎng)絡(luò)上的爆炸式同步現(xiàn)象自2011年被發(fā)現(xiàn)以來(lái)立刻成為了一個(gè)新的熱點(diǎn)問(wèn)題,作為復(fù)雜網(wǎng)絡(luò)上動(dòng)力學(xué)臨界現(xiàn)象的代表而受到了極大關(guān)注。最早給出的爆炸式同步要滿足兩個(gè)必要條件：1、拓?fù)浣Y(jié)構(gòu)為無(wú)標(biāo)度網(wǎng)；2、振子的本征頻率與節(jié)點(diǎn)度成正相關(guān)。這就使得爆炸式同步現(xiàn)象的出現(xiàn)條件非�？量�。為了能更全面地理解爆炸式同步現(xiàn)象,本文以探尋其產(chǎn)生機(jī)制為出發(fā)點(diǎn),以數(shù)值模擬和理論分析相結(jié)合,研究復(fù)雜網(wǎng)絡(luò)上爆炸式同步現(xiàn)象的產(chǎn)生條件,考察同步化過(guò)程中的微觀變化,在此基礎(chǔ)上提出控制的策略,并取得了以下主要成果：1、提出以振子本征頻率做為耦合權(quán)重的新模型,將前人所研究的振子本征頻率等于節(jié)點(diǎn)度的模型歸為該模型的一個(gè)特例,并將爆炸式同步的產(chǎn)生條件由嚴(yán)苛的節(jié)點(diǎn)本征頻率與節(jié)點(diǎn)度成正相關(guān)且網(wǎng)絡(luò)結(jié)構(gòu)必須為無(wú)標(biāo)度網(wǎng),拓寬到了一般的復(fù)雜網(wǎng)絡(luò)和一般的本征頻率分布。2、通過(guò)分析系統(tǒng)中每個(gè)振子間的關(guān)聯(lián)性在同步化過(guò)程中的變化,刻畫了爆炸式同步現(xiàn)象中系統(tǒng)內(nèi)同步簇團(tuán)的形成過(guò)程,提出可以用動(dòng)力學(xué)空間中的爆炸式滲流過(guò)程來(lái)看待爆炸式同步現(xiàn)象的觀點(diǎn),并通過(guò)類比爆炸式滲流的產(chǎn)生原因,給出了爆炸式同步現(xiàn)象出現(xiàn)的判據(jù)：抑制規(guī)則(suppressive rule)。3、將發(fā)現(xiàn)的“抑制規(guī)則”推廣運(yùn)用到多層網(wǎng)上,提出了以振子局部的同步序參量作為耦合權(quán)重的模型,從而首次將爆炸式同步的研究推廣到多層網(wǎng)和自適應(yīng)網(wǎng)絡(luò)上。4、利用模型中自然存在的雙穩(wěn)態(tài),通過(guò)設(shè)計(jì)耦合方式與權(quán)重,在研究爆炸式同步現(xiàn)象的模型中觀察到了奇異態(tài)(Chimera state),并提出系統(tǒng)具有雙穩(wěn)態(tài)很可能是這兩種重要現(xiàn)象的聯(lián)系。5、研究了爆炸式同步現(xiàn)象的反問(wèn)題：如何抑制系統(tǒng)中有害的爆炸式同步現(xiàn)象。通過(guò)在系統(tǒng)中引入反對(duì)者(contrarian),將系統(tǒng)原本的不連續(xù)同步相變變?yōu)檫B續(xù)相變,并在模型網(wǎng)絡(luò)和真實(shí)網(wǎng)絡(luò)中都證實(shí)了這是一種能有效抑制系統(tǒng)中爆炸式同步現(xiàn)象的策略。
[Abstract]:Explosive synchronization (explosive synchronization) phenomenon indicates that the process of complex networks from chaotic state to synchronous state is a discontinuous, first order phase transition with hysteresis, which is much more continuous with the known phase transition, and the conclusion of the two stage phase transition without hysteresis is completely different. In the image, the system has two steady states and the switching between two steady states is fast and discontinuous. This is highly similar to many sudden phenomena in the reality, such as the epileptic outbreak in the brain and cascading failure in the power grid. Since the explosive percolation problem since 2009 is hot in the complex network field, the complex network is on the complex network The explosive synchronization has become a new hot issue since it was discovered in 2011. It has received great attention as the representative of the dynamic critical phenomenon on the complex network. The earliest explosive synchronization should satisfy two necessary conditions: 1, the topological structure is the scale-free network, and 2, the eigenfrequency of the oscillator is in positive phase with the degree of node. In order to understand the phenomenon of explosive synchronization more comprehensively, in order to understand the phenomenon of explosive synchronization more comprehensively, this paper aims at exploring the mechanism of its generation as the starting point, combining numerical simulation and theoretical analysis to study the production conditions of explosive synchronization on complex networks, and investigate the microscopic changes in the process of synchronization. On this basis, the control strategy is proposed, and the following main achievements are obtained: 1, a new model is proposed, which takes the eigenfrequency of the oscillator as the coupling weight, and the model of the oscillator eigenfrequency equal to the node degree is classified as a special case of the model, and the conditions for the generation of the explosive synchronization are from the severe node eigenfrequency and the node degree. The network structure is positively correlated and the network structure must be extended to the scale-free network, which extends to the general complex network and the general eigenfrequency distribution.2. By analyzing the changes in the synchronization process of the correlation between every oscillator in the system, the formation process of the synchronous cluster in the system of explosive synchronization is depicted, and it is proposed that the dynamic space can be used in the dynamic space. The explosion type seepage process takes the viewpoint of the explosive synchronization phenomenon, and gives the criterion of the occurrence of the explosion synchronization phenomenon through the cause of the analogical explosive percolation. The suppression rule (suppressive rule).3 is used to apply the discovery of the "suppression rule" to the multi-layer network, and the synchronous order parameter of the local oscillator is proposed. The model of coupling weight is used for the first time to extend the research of explosive synchronization to.4 on multi-layer network and adaptive network. By using the natural bistable state in the model, the singular state (Chimera state) is observed in the model of the explosion synchronization phenomenon by designing the coupling mode and weight, and it is suggested that the system has bistable state is very likely to be The connection between the two important phenomena,.5, has studied the inverse problem of explosive synchronization: how to suppress the harmful explosive synchronization in the system. By introducing an opponent (contrarian) into the system, the original discontinuous phase transition of the system is transformed into a continuous phase transformation, and it is proved that this is a kind of energy in both the model network and the real network. A strategy to effectively suppress explosive synchronization in the system.
【學(xué)位授予單位】：華東師范大學(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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