Zhang Junjie, Liu Caixia, Liu Shuxin, Wang Kai, Zang Weifei
Institute of Information Technology, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China.
Institute of System Engineering, Academy of Military Sciences, Beijing 100091, China.
Entropy (Basel). 2024 Aug 16;26(8):693. doi: 10.3390/e26080693.
Prior research on cascading failures within interdependent networks has predominantly emphasized the coupling of nodes. Nevertheless, in practical networks, interactions often exist not just through the nodes themselves but also via the connections (edges) linking them, a configuration referred to as edge-coupled interdependent networks. Past research has shown that introducing a certain percentage of reinforced nodes or connecting edges can prevent catastrophic network collapses. However, the effect of reinforced inter-layer links in edge-coupled interdependent networks has yet to be addressed. Here, we develop a theoretical framework for studying percolation models in edge-coupled interdependent networks by introducing a proportion of reinforced inter-layer links and deriving detailed expressions for the giant and finite components and the percolation phase transition threshold. We find that there exists a required minimum proportion of the reinforced inter-layer links to prevent abrupt network collapse, which serves as a boundary to distinguish different phase transition types of a network. We provide both analytical and numerical solutions for random and scale-free networks, demonstrating that the proposed method exhibits superior reinforcement efficiency compared to intra-layer link reinforcement strategies. Theoretical analysis, simulation results, and real network systems validate our model and indicate that introducing a specific proportion of reinforced inter-layer links can prevent abrupt system failure and enhance network robustness in edge-coupled interdependent networks.
先前关于相互依存网络中级联故障的研究主要强调节点的耦合。然而，在实际网络中，相互作用往往不仅通过节点本身存在，还通过连接它们的边（连接）存在，这种结构被称为边耦合相互依存网络。过去的研究表明，引入一定比例的强化节点或连接边可以防止灾难性的网络崩溃。然而，边耦合相互依存网络中强化层间链接的效果尚未得到研究。在此，我们通过引入一定比例的强化层间链接并推导巨分量和有限分量以及渗流相变阈值的详细表达式，建立了一个用于研究边耦合相互依存网络中渗流模型的理论框架。我们发现，存在一个防止网络突然崩溃所需的强化层间链接的最小比例，它作为区分网络不同相变类型的边界。我们为随机网络和无标度网络提供了解析解和数值解，表明与层内链接强化策略相比，所提出的方法具有更高的强化效率。理论分析、模拟结果和实际网络系统验证了我们的模型，并表明引入特定比例的强化层间链接可以防止系统突然故障并增强边耦合相互依存网络的鲁棒性。
