复杂网络上的爆炸式同步

发布时间：2018-05-30 19:23

本文选题：复杂网络 + 非线性动力学　；参考：《华东师范大学》2016年博士论文

【摘要】：爆炸式同步(explosive synchronization)现象指的是复杂网络从混乱状态变化到同步状态的过程是一个不连续的、伴随着磁滞现象的一级相变过程,这与人们所熟知的同步相变多为连续的、无磁滞的二级相变的结论截然不同。在爆炸式同步现象中,系统具有两个稳态并且在两个稳态间的切换是快速,不连续的,这与现实中的很多突发性现象如大脑中的癫痫病爆发以及电网中的级联失效等有高度相似性。由于2009年以来爆炸式渗流问题在复杂网络领域的火热,复杂网络上的爆炸式同步现象自2011年被发现以来立刻成为了一个新的热点问题,作为复杂网络上动力学临界现象的代表而受到了极大关注。最早给出的爆炸式同步要满足两个必要条件：1、拓扑结构为无标度网；2、振子的本征频率与节点度成正相关。这就使得爆炸式同步现象的出现条件非常苛刻。为了能更全面地理解爆炸式同步现象,本文以探寻其产生机制为出发点,以数值模拟和理论分析相结合,研究复杂网络上爆炸式同步现象的产生条件,考察同步化过程中的微观变化,在此基础上提出控制的策略,并取得了以下主要成果：1、提出以振子本征频率做为耦合权重的新模型,将前人所研究的振子本征频率等于节点度的模型归为该模型的一个特例,并将爆炸式同步的产生条件由严苛的节点本征频率与节点度成正相关且网络结构必须为无标度网,拓宽到了一般的复杂网络和一般的本征频率分布。2、通过分析系统中每个振子间的关联性在同步化过程中的变化,刻画了爆炸式同步现象中系统内同步簇团的形成过程,提出可以用动力学空间中的爆炸式渗流过程来看待爆炸式同步现象的观点,并通过类比爆炸式渗流的产生原因,给出了爆炸式同步现象出现的判据：抑制规则(suppressive rule)。3、将发现的“抑制规则”推广运用到多层网上,提出了以振子局部的同步序参量作为耦合权重的模型,从而首次将爆炸式同步的研究推广到多层网和自适应网络上。4、利用模型中自然存在的双稳态,通过设计耦合方式与权重,在研究爆炸式同步现象的模型中观察到了奇异态(Chimera state),并提出系统具有双稳态很可能是这两种重要现象的联系。5、研究了爆炸式同步现象的反问题：如何抑制系统中有害的爆炸式同步现象。通过在系统中引入反对者(contrarian),将系统原本的不连续同步相变变为连续相变,并在模型网络和真实网络中都证实了这是一种能有效抑制系统中爆炸式同步现象的策略。
[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.
【学位授予单位】：华东师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O157.5

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