基于超图理论的超网络相继故障及应用研究

The failure of human lifeline system seriously affects people's production and life, and bring unmeasured loss to human society. The failure at node or on the edge of the network, will spread in the whole network, trigger cascading failure of network, eventually lead to the entire network collapse disastrous consequences. . The project is based on the hypergraph theory put forward suitable capacity-load cascading failure model and coupled map lattice cascading failure model to describe cascading failure behavior of hypernetwork; Based on the hyper-graph theory, the project put forward capacity-load cascading failure model and coupled map lattice cascading failure model which are suitable to describe cascading failure behavior of hypernetwork;Research cascading failure behavior occuring in the deterministic hypernetworks and random hypernetworks to analyze the cascading failure process of hypernetwork and to reveal the failure mechanism, the diffusion process of failure and influence factors; Calculate capacity threshold and disturbance threshold which lead hypernetwork to global collapse; Find deterministic hypernetworks which have optimal robust, discover the impacts of the homogeneity of hyperedge on robustness of random hypernetwork, and analyze the networks’ ability to resist different attacks. . The research results of cascading failure on hypernework are important to understand the hypernetwork cascading failure phenomenon in the further, and essential for effective control and prevention the occurrence and spread of failure on the hypernetwork. In addition, they are of important reference value and significance to optimize hypernetwork structure, reduce and prevent the failure damage.

发生在人类生命线系统网络上的故障严重影响着人们的生产和生活，给人类社会带来了不可估量的损失。网络中节点或边上的故障，会在整个网络中扩散，引发网络的相继故障，最终会导致整个网络崩溃，带来灾难性的后果。. 本项目基于超图理论提出适合描述超网络相继故障行为的容量-负荷模型和耦合映像格子模型；研究确定性超网络和随机超网络的相继故障行为，分析它们的相继故障进程；揭示超网络相继故障的发生机理、扩散过程及影响因素；计算使超网络达到全局崩溃的阈值的理论解；发现鲁棒性最优的确定性超网络结构和超边的均匀性对随机超网络鲁棒性的影响，并对实证超网络的相继故障行为进行应用研究。 . 超网络相继故障的相关研究结果对进一步理解发生在超网络上的相继故障有重要的作用，对有效控制和预防超网络相继故障的发生和蔓延至关重要；此外，对优化网络结构、减轻和防止相继故障带来的危害有重要的参考价值和意义。

网络中节点或边上的故障，会在整个网络中扩散，引发网络的相继故障，最终会导致整个网络崩溃，带来灾难性的后果。本项目基于超图理论研究了超网络的相继故障行为。研究了超网络上的相继故障模型，并研究了k均匀无标度超网络、确定性均匀超网络、相互依存的耦合网络等网络的相继故障行为；研究了超网络相继故障的发生机理、扩散过程、影响因素以及超网络的全局崩溃阈值；研究了与超网络鲁棒性相关的另一测度—超网络的可靠性。通过本项目的研究，获得了k均匀超网络、非均匀超网、确定性超网络的构建方法；提出了适合描述超网络和普通网络相继故障行为的相继故障模型；并获得了超网络相继故障进程的特点及全局崩溃阈值的解析解；提出了一类特殊超网络可靠性测度的计算方法；并获得了可靠性最优和最差的超网络结构。超网络相继故障的相关研究结果对进一步理解发生在超网络上的相继故障有重要的作用，对有效控制和预防超网络相继故障的发生和蔓延至关重要；此外，对优化网络结构、减轻和防止相继故障带来的危害有重要的参考价值和意义。同时，本课题的相关研究结果进一步完善了超网络的理论体系，为进一步开展超网络上的其它动力学性质的研究提供了借鉴和参考。