Dong Gaogao, Chen Yan, Wang Fan, Du Ruijin, Tian Lixin, Stanley H Eugene
Institute of Applied System Analysis, Faculty of Science, Jiangsu University, Zhenjiang, 212013 Jiangsu, China.
School of Mathematical Sciences, Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing Normal University, Jiangsu 210023, People's Republic of China.
Chaos. 2019 Jul;29(7):073107. doi: 10.1063/1.5093074.
Interdependent networks as an important structure of the real system not only include one-to-one dependency relationship but also include more realistic undirected multiple interdependent relationship. The study on interdependent networks plays an important role in designing more resilient real systems. Here, we mainly focus on the case of interdependent networks with a multiple-to-multiple correspondence of interdependent nodes by generalizing feedback and nonfeedback conditions. We develop a new mathematical framework and study numerically and analytically the percolation of interdependent networks with partial multiple-to-multiple dependency links by using percolation theory. By analyzing the process of cascading failure, the size of the giant component and the critical threshold are analytically obtained and testified by simulation results for couple Erdös-Re˙nyi and scale-free networks. The results imply that the system shows a discontinuous phase transition for different coupling strengths. We find that the system becomes more resilient and easy to defend by increasing the coupling strength and the connectivity density. Our model has the potential to shed light on designing more resilient real-world dependent systems.
相互依存网络作为现实系统的一种重要结构，不仅包括一对一的依赖关系，还包括更符合实际的无向多重相互依存关系。对相互依存网络的研究在设计更具弹性的现实系统中起着重要作用。在此，我们主要通过推广反馈和非反馈条件，关注具有相互依存节点多对多对应关系的相互依存网络情况。我们开发了一个新的数学框架，并利用渗流理论对具有部分多对多依赖链接的相互依存网络的渗流进行了数值和解析研究。通过分析级联故障过程，解析得出了巨组件的大小和临界阈值，并通过对耦合的厄尔多斯 - 雷尼网络和无标度网络的模拟结果进行了验证。结果表明，对于不同的耦合强度，系统呈现出不连续的相变。我们发现，通过增加耦合强度和连通性密度，系统变得更具弹性且更易于防御。我们的模型有潜力为设计更具弹性的现实世界依赖系统提供启示。
