几类复杂网络与超网络的相继故障及可控性研究

发布时间：2018-04-19 05:14

本文选题：和谐统一混合择优网络 + κ均匀无标度超网络　；参考：《陕西师范大学》2016年博士论文

【摘要】：随着当代科学技术的不断发展,网络充满了人类社会的各个领域,并日益影响着人们的生产和生活.对各种复杂网络建模和拓扑性质的分析使人们对复杂网络有了深入的了解,而复杂网络动力学性质的研究是复杂网络研究的终极目标之一,对网络动力学性质的研究可以帮助人们更清楚的认识网络的特性,解决很多实际问题.例如北美大停电事故体现了网络的相继故障行为,而复杂系统的信号输入问题又可以用网络的可控性来解决等.目前对网络相继故障、同步、控制和传播等动力学性质的研究已成为网络科学研究的主题和热点.本文基于复杂网络理论、超图和超网络理论等多学科领域的知识和方法,研究了一类和谐统一混合择优网络的相继故障行为.针对现实超网络相继故障的特点研究κ均匀无标度超网络的相继故障行为.讨论了度序列相同的一类确定性网络的可控性,并提出了一类确定性超网络的构建方法,探讨了这类确定性超网络的可控性.主要内容如下:(1)分析了一类和谐统一混合择优网络耦合映像格子的相继故障行为,获得了该网络抵抗随机攻击和蓄意攻击的能力,发现了测量该网络鲁棒性的测度.另外,理论推导了使网络达到全局崩溃所需的扰动阈值的近似值,并和实验结果进行了对比,验证了理论分析的有效性.(2)针对现实中的快递超网络和电子元件超网络上相继故障的扩散特点,利用超图理论,首次提出了分析这两类超网络相继故障行为的方法.并分析了均匀无标度超网络耦合映像格子的相继故障行为及这类超网络遭受随机攻击和蓄意攻击时的鲁棒性及影响超网络鲁棒性的因素,并与普通网络的鲁棒性进行了对比.同时给出了 κκ均匀无标度超网络扰动阈值的理论近似值,并和实验结果进行了比较.(3)基于超网络的超邻接矩阵和联合度首次提出了一种适合描述超网络相继故障行为的新模型,并利用该模型仿真模拟了 3均匀无标度超网络的相继故障行为,分析了该超网络的鲁棒性及其影响因素.明确了3均匀无标度超网络扰动阈值的理论近似值,通过和实验数据的对比验证了理论分析的有效性.(4)利用精确可控性理论,分析了一类度序列相同的确定性(x,y)-花网络的可控性,给出了这类网络的最小驱动节点集的精确解;同时,通过对(x,y)-花网络进行扩展,首次提出了一类确定性2κ均匀超(1,3)-花网络的构建算法,结合超图理论和精确可控性理论,首次分析了这类确定性超网络的可控性.
[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.
【学位授予单位】：陕西师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O157.5

【参考文献】