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复杂系统的功能通过节点之间的连接而维持, 部分节点的失效会对系统的连通性造成破坏而影响整体的功能. 除此之外, 部分节点还会通过隐含依赖性而形成“依赖组”, 其中一个节点的失效会对依赖组中其余节点造成损害. 本文研究了“依赖组”的平均规模, 规模分布和节点之间的依赖强度对网络级联失效和鲁棒性的影响. 通过数值模拟和理论分析发现, 网络的级联失效在尺度层次上可以分为“组内级联”和“组间级联”两个过程. 在组内级联过程中, 一个节点的失效会通过节点之间的依赖性对组内其他节点造成破坏, 从而诱发更多节点的失效, 进而产生更大的破坏力. 在组间级联过程中, 失效节点会引起网络发生破碎而导致组外节点脱离网络巨分支而失效, 这就引起了失效节点的跨依赖组传播. 在这两种失效过程的共同作用下, 网络在级联失效过程中会表现出连续和不连续的两种渗流相变现象, 这两种相变现象的发生与节点间的依赖强度、网络度分布以及依赖组规模分布有关. 这意味着通过控制依赖组的特征, 如依赖组中节点之间的依赖强度或依赖组规模分布, 可以避免系统突然崩溃进而提高网络的鲁棒性.In real complex systems, the overall function is maintained through the connections among nodes. Failures of some nodes may destroy the connectivity of the system and thus damage the function of the system. In some complex systems, some nodes can form “interdependency groups” through hidden interdependency. The failure of one node may damage the rest of the nodes in the interdependency group. In this paper, we investigate the effects of the interdependency strength of the nodes, the size distribution, and the size of the interdependency groups on the cascading dynamics and the robustness of complex networks. Through numerical simulation and theoretical analysis, it is found that the cascading failures of the networks can be divided into two processes at a scale level: “intra-group cascading” and “inter-group cascading”. In the intra-group cascading process, the failure of one node will result in damage to the other nodes in the group through the interdependence among nodes, thus inducing more nodes to be unworkable and resulting in greater destructive force. In the inter-group cascading process, the failed nodes will cause the networks to be fragmented, which leads some nodes outside the interdependency group to isolate from the giant component and go to failure. Under the synergistic effects of these two processes, it is found that there are continuous and discontinuous phase transition phenomena in the cascade dynamics of the network. The occurrence of these two kinds of phase transition phenomena is related to the interdependency strength of nodes, the network degree distribution and the size distribution of the interdependency group. This means that by controlling the characteristics of interdependency groups, such as the interdependence strength of the nodes in the interdependency group or the size distribution of interdependency groups, the system can avoid collapsing suddenly and thus the robustness of the network can be improved.
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Keywords:
- interdependency group/
- weak interdependence/
- cascading failure/
- giant component/
- robustness
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