Depth Penetration and Scope Extension of Failures in the Cascading of Multilayer Networks

Wen-Jun Jiang,Chun-Xiao Jia,Run-Ran Liu

doi:10.1155/2020/3578736

Abstract

Real-world complex systems always interact with each other, which causes these systems to collapse in an avalanche or cascading manner in the case of random failures or malicious attacks. The robustness of multilayer networks has attracted great interest, where the modeling and theoretical studies of which always rely on the concept of multilayer networks and percolation methods. A straightforward and tacit assumption is that the interdependence across network layers is strong, which means that a node will fail entirely with the removal of all links if one of its interdependent nodes in other network layers fails. However, this oversimplification cannot describe the general form of interactions across the network layers in a real-world multilayer system. In this paper, we reveal the nature of the avalanche disintegration of general multilayer networks with arbitrary interdependency strength across network layers. Specifically, we identify that the avalanche process of the whole system can essentially be decomposed into two microscopic cascading dynamics in terms of the propagation direction of the failures: depth penetration and scope extension. In the process of depth penetration, the failures propagate from layer to layer, where the greater the number of failed nodes is, the greater is the destructive power that will emerge in an interdependency group. In the process of scope extension, failures propagate with the removal of connections in each network layer. Under the synergy of the two processes, we find that the percolation transition of the system can be discontinuous or continuous with changes in the interdependency strength across network layers, which means that a sudden system-wide collapse can be avoided by controlling the interdependency strength across network layers. Our work not only reveals the microscopic mechanism of global collapse in multilayer infrastructure systems but also provides stimulating ideas on intervention programs and approaches for cascade failures.

Highlights

Many real-world complex systems, both natural [1] and man made [2,3,4,5], can be described as multilayer or interdependent networks given the existence of different levels of interdependence across network layers
For both three- and four-layer random networks, the manners of percolation transition are classified as discontinuous and continuous by a critical value of αc, and the critical value of αc only depends on the number of network layers M in a system, which coincides the theoretical result provided by pcII ≈ 0.307
Conclusions and Discussion e interdependence of real multilayer networks is generally weak in layer-to-layer interactions, where the failure of one node usually does not result in failures of interdependent nodes across all network layers

Summary

Introduction

Many real-world complex systems, both natural [1] and man made [2,3,4,5], can be described as multilayer or interdependent networks given the existence of different levels of interdependence across network layers. Recent theoretical studies on networks with two or more layers show that when the nodes in each network are interdependent on the nodes in other networks, even small initial failures can propagate back and forth and lead to the abrupt collapse of the whole system [5,6,7,8,9,10]. In this sense, multilayer networks are more fragile than single-layer networks in resisting the propagation of initial failures [6]. Some features of real interdependent systems, such as spatial constraints [26,27,28,29,30], clustering [31, 32], and degree distribution [33, 34], enhance the robustness and mitigate cascading failures of interdependent networks

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Conclusion