互连网络的结构鲁棒性和传播动力学研究

发布时间：2018-03-11 21:24

本文选题：复杂网络　切入点：网络互连　出处：《中国矿业大学》2016年硕士论文　论文类型：学位论文

【摘要】：随着社会和科技的发展,现实社会中涌现出大量小规模网络逐渐依附到大规模网络上的现象,并逐渐形成更大规模的互连网络。这种互连行为所形成的互连网络与原始大网络的拓扑结构和动力学行为特性的差异,得到越来越多的关注和研究。基于上述互连行为的特点,本文提出了这种互连方式(稠密的小网络和稀疏的大网络之间的互连)下的互连网络模型,并对该互连模型的结构鲁棒性和传播动力学特性等动力学行为进行研究,为实现分析、控制和利用复杂系统提供重要的指导意义。网络结构鲁棒性是复杂网络在受到破坏时能否持续稳定运行的一种体现,对于网络良好运行至关重要,已经成为系统在不确定性和危机出现的情况下能否生存的关键所在。采用自然连通度和代数连通度等衡量指标以及逾渗分析方法,本文对所提出的互连网络模型的结构鲁棒性进行了分析研究,得出了三种不同结论:1)整个互连网络的自然连通度相较于原始大网络得到大幅提升,意味着在自然连通度的衡量下网络的结构鲁棒性提高了;2)整个互连网络的代数连通度相较于原始大网络明显减小,表明从代数连通度的角度考虑,网络的结构鲁棒性是降低的;3)整个互连网络在随机攻击下的逾渗阈值和巨分量与原始大网络相近,反映了在随机攻击情况下,网络的结构鲁棒性并没有发生明显变化。因为传播速度快和对社会影响大,病毒传播一直是复杂网络传播动力学特性研究中的重要研究方向之一,量化和控制病毒传播及其所引起的损失问题受到越来越多的关注。基于非线性动力学系统模型(NLDS)和矩阵论等数学工具,对本文提出的互连网络模型上的病毒传播阈值和传播过程损失进行了分析研究,结果表明:1)整个互连网络中病毒传播阈值相较于原始大网络明显减小,这将意味着病毒在互连网络中更容易爆发;2)整个互连网络中的病毒传播所带来的总损失相较于原始大网络几乎不变,这意味这种互连行为在大幅降低整体网络病毒传播阈值的同时没有改变其传播总损失。
[Abstract]:With the development of society and technology, the emergence of a large number of small scale network gradually attached to the large-scale network phenomenon in the social reality, and gradually formed a larger difference. The interconnection network topological structure and dynamic behavior of the formation of the interconnection behavior of the interconnection network with the original network, has gained more and more attention and research. The characteristics of the interconnection based on behavior, this paper puts forward the interconnection mode (interconnection between the dense network of small and sparse network of interconnection network) model, and carries out research on the interconnection structure of the robustness and the propagation dynamics of dynamic behavior, in order to realize the analysis, control and use of complex system provides important significance. Network structure robustness is a complex network can reflect the continued stable operation in the event of damage, the network is very important To, has become the key to survival in the system uncertainty and crisis situations. The natural connectivity and algebraic connectivity index and percolation analysis method, the structure of the proposed robust interconnection network model of the analysis, put forward three different conclusions: 1) the the interconnection network of natural connectivity compared to the original network has increased substantially, means that the natural connectivity measure of structural robustness under network has been improved; 2) the algebraic connectivity of the interconnection network compared to the original network is obviously reduced, that from the algebraic connectivity point of view, the robustness of the network structure is reduced; 3) the interconnection network under random attack under the percolation threshold and the giant component with the original network similar to that reflected in the random attack case, robust network and did not happen The obvious change. Because of high propagation speed and great impact on society, the spread of the virus has been one of the important research direction of research on dynamic characteristics of propagation in complex networks, loss quantification and control the spread of the virus and caused by more and more attention. Based on nonlinear dynamic system model (NLDS) and matrix theory and other mathematical tools to the interconnection network model proposed in this paper on the spread of the virus and propagation loss threshold were analyzed, the results show that: 1) the spread of the virus in the interconnection network threshold compared to the original network significantly reduced, this will mean that the virus in the interconnection network more easily burst; 2) the total loss caused by the spread of the virus across the interconnection in the network compared to the original network is almost the same, which means the interconnection behavior in significantly reducing the overall network virus spreading threshold without changing its spread Total loss.

【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP393.03;O157.5

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