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Abstract Cascading failures are emergent phenomena on interdependent networks and plenty of models have been proposed to explore the features of cascading failures. However, few of them focus on energy-supported dependence relations between interdependent networks including control nodes. In this paper, a load-based energy-supported cascading failure model is proposed on interdependent networks, where the energy control factor λ and control nodes are considered. According to the numerical simulations, it is found that as the energy control factor λ increases, both interdependent Erdős–Rényi (ER) networks and scale-free (SF) networks become more vulnerable. Meanwhile, with the increase of energy control factor λ , interdependent SF networks become more robust than ER networks against random failures. In addition, increasing the power exponent γ can improve the robustness of interdependent SF networks. Finally, although coupling preferences and control node setting strategies have few impacts on cascading failures on interdependent ER networks, the assortative coupling preference (AC) and betweenness control node setting strategy (BS) can improve the robustness of interdependent SF networks. Highlights • An energy-supported cascading failure model is proposed on interdependent networks. • Increasing factor λ makes interdependent SF networks more robust than ER networks. • Increasing exponent γ improves the robustness of interdependent SF networks. • The AC and BS can improve the robustness of interdependent SF networks. [ABSTRACT FROM AUTHOR]

Abstract A concept of bypass rewiring on directed networks is proposed, and random bypass rewiring on infinite directed random networks is analytically and numerically investigated with double generating function formalisms and simulations. As a result, it is derived that random bypass rewiring makes infinite directed (undirected) random networks extremely robust for arbitrary occupation probabilities if and only if in-degree of every node except a fixed number of nodes is equal to the out-degree (every node except a finite number of nodes has even degree); random bypass rewiring can make the percolation threshold 0 on infinite directed (undirected) random networks. From the results on infinite random networks, it is generalized that a finite network has a strongly connected spanning subnetwork which has an Eulerian path or cycle if and only if there exists an way of bypass rewiring to make the finite network extremely robust for every combination of removed nodes; Eulerian networks are extremely robust with bypass rewiring for every combination of removed nodes. The generalized results say that bypass rewiring improves connectivity and robustness of not only infinite networks but also real-world networks, like the Internet, with a finite number of nodes. Highlights • A concept of bypass rewiring on directed networks is proposed. • Random bypass rewiring can guarantee extreme robustness of random networks. • Bypass rewiring can make the percolation threshold 0. • Bypass rewiring guarantees extreme robustness of Eulerian networks. • Bypass rewiring can guarantee extreme robustness of the Internet topology. [ABSTRACT FROM AUTHOR]

Cascading failures are widely found in hyper-networks. In this paper, a new cascading failure model based on couple map lattice is proposed in terms of the hyper-adjacent matrix and joint degree. The cascading failure model is rather universal describing the cascading failure behavior of k uniform hyper-network and many typical complex networks. Simulation results show that 3 uniform scale-free hyper-network is robust against random attacks but is vulnerable to deliberate attacks. In addition, a scale-free hyper-network is more robust than a general complex network against the same attack. Finally, an approximate solution to the disturbance threshold of k uniform scale-free hyper-network is obtained. [ABSTRACT FROM AUTHOR]

Cascade phenomenon may lead to catastrophic disasters which extremely imperil the network safety or security in various complex systems such as communication networks, power grids, social networks and so on. In some flow-based networks, the load of failed nodes can be redistributed locally to their neighboring nodes to maximally preserve the traffic oscillations or large-scale cascading failures. However, in such local flow redistribution model, a small set of key nodes attacked subsequently can result in network collapse. Then it is a critical problem to effectively find the set of key nodes in the network. To our best knowledge, this work is the first to study this problem comprehensively. We first introduce the extra capacity for every node to put up with flow fluctuations from neighbors, and two extra capacity distributions including degree based distribution and average distribution are employed. Four heuristic key nodes discovering methods including High-Degree-First (HDF), Low-Degree-First (LDF), Random and Greedy Algorithms (GA) are presented. Extensive simulations are realized in both scale-free networks and random networks. The results show that the greedy algorithm can efficiently find the set of key nodes in both scale-free and random networks. Our work studies network robustness against cascading failures from a very novel perspective, and methods and results are very useful for network robustness evaluations and protections. [ABSTRACT FROM AUTHOR]

In this paper, the performance of metro networks is studied from a network science perspective. We review the structural efficiency of metro networks on the basis of a passenger’s intuitive routing strategy that optimizes the number of transfers and the distance traveled.A new node centrality measure, called node occupying probability , is introduced for evaluating the level of utilization of stations. The robustness of a metro network is analyzed under several attack scenarios. Six metro networks (Beijing, London, Paris, Hong Kong, Tokyo and New York) are compared in terms of the node occupying probability and a few other performance parameters. Simulation results show that the New York metro system has better topological efficiency, the Tokyo and Hong Kong systems are the most robust under random attack and target attack , respectively. [ABSTRACT FROM AUTHOR]

An assembly supply chain network (ASCN) is composed of manufacturers located in different geographical regions. To analyze the robustness of this ASCN when it suffers from catastrophe disruption events, we construct a cascading failure model of risk propagation. In our model, different disruption scenarios s are considered and the probability equation of all disruption scenarios is developed. Using production capability loss as the robustness index (RI) of an ASCN, we conduct a numerical simulation to assess its robustness. Through simulation, we compare the network robustness at different values of linking intensity and node threshold and find that weak linking intensity or high node threshold increases the robustness of the ASCN. We also compare network robustness levels under different disruption scenarios. [ABSTRACT FROM AUTHOR]

The robustness of complex network is a core issue in complex network research. We agree that not all overload nodes will be removed from the network in real networks because some effective measures can be taken to protect them. But only a few researches consider this issue. Based on previous researches, we propose a cascading model with an improved breakdown probability. Different from previous breakdown probability model, the current model brings in some parameters to explore the optimal distribution strategy of the protection resources. Furthermore, we quantify the allocation of the protection resources. We explore the relationship between the parameters of our cascading model and the robustness of three networks (two typical networks and one real network), based on which we find out the optimal value of the parameter. It in turn helps us to quantify the allocation of protection resources and form an optimal protection strategy. Our work may be helpful for improving the robustness of complex networks. [ABSTRACT FROM AUTHOR]

The problem of finding the best strategy to attack a network or immunize a population with a minimal number of nodes has attracted much current research interest. The assessment of node importance has been a fundamental issue in the research of complex networks. In this paper, we propose a new concept called mapping entropy (ME) to identify the importance of a node in the complex network. The concept is established according to the local information which considers the correlation among all neighbors of a node. We evaluate the efficiency of the centrality by static and dynamic attacks on standard network models and real-world networks. The simulation result shows that the new centrality is more efficient than traditional attack strategies, whether it is static or dynamic. [ABSTRACT FROM AUTHOR]

A supply chain network is a typical interdependent network composed of an undirected cyber-layer network and a directed physical-layer network. To analyze the robustness of this complex interdependent supply chain network when it suffers from disruption events that can cause nodes to fail, we use a cascading failure process that focuses on load propagation. We consider load propagation via connectivity links as node failure spreads through one layer of an interdependent network, and we develop a priority redistribution strategy for failed loads subject to flow constraint. Using a giant component function and a one-to-one directed interdependence relation between nodes in a cyber-layer network and physical-layer network, we construct time-varied functional equations to quantify the dynamic process of failed loads propagation in an interdependent network. Finally, we conduct a numerical simulation for two cases, i.e., single node removal and multiple node removal at the initial disruption. The simulation results show that when we increase the number of removed nodes in an interdependent supply chain network its robustness undergoes a first-order discontinuous phase transition, and that even removing a small number of nodes will cause it to crash. [ABSTRACT FROM AUTHOR]

Interdependent network models are often used to show how one network has an effect on another network through dependencies. In this paper, we propose a novel interdependent network model which consists of two individual networks with unequal numbers of nodes and one-to-multiple weighted dependency links between the two networks. Based on realistic assumptions, this model differs from previous works that considered equal numbers of nodes in the two networks and identical dependency links. We formulate an optimization problem to allocate dependency links using least resources. This novel model enhances the practicability of traditional cyber–physical system structures, but it makes the dependency link deployment problem more complex and the optimization problem cannot be solved in large networks. To overcome this problem, we propose a new algorithm based on a revised network flow method. Extensive simulations on random networks and real networks show that our deployment method produces topologies that are more robust than the ones obtained by other deployment techniques. Results indicate that our algorithm is efficient and cost-effective in designing robust interdependent networks, and our deployment method is suitable for networks of any size. [ABSTRACT FROM AUTHOR]

Identifying the most influential individuals spreading ideas, information, or infectious diseases is a topic receiving significant attention from network researchers, since such identification can assist or hinder information dissemination, product exposure, and contagious disease detection. Hub nodes, high betweenness nodes, high closeness nodes, and high k -shell nodes have been identified as good initial spreaders. However, few efforts have been made to use node diversity within network structures to measure spreading ability. The two-step framework described in this paper uses a robust and reliable measure that combines global diversity and local features to identify the most influential network nodes. Results from a series of Susceptible–Infected–Recovered (SIR) epidemic simulations indicate that our proposed method performs well and stably in single initial spreader scenarios associated with various complex network datasets. [ABSTRACT FROM AUTHOR]

This article studies the issue of uniform synchronization for chaotic dynamical systems via event-triggered impulsive control (ETIC). The synchronization scheme is executed by designing ETIC with three levels of event-triggering conditions. Under the designed ETIC, the uniform exponential synchronization is achieved for master–slave chaotic systems. It shows the uniform synchronization via ETIC is robust with respect to time delays in ETIC. Moreover, the notions including rate of control and cost of control are proposed for comparisons with uniform synchronization via classic impulsive control (CIC) which is time-triggered impulsive control. The chaotic Lorenz system is used to test the performances of uniform synchronization via ETIC and CIC. The specific ETIC and CIC for uniform synchronization of master–slave Lorenz systems are designed and the numerical simulations of synchronizations via ETIC and CIC are given. It is shown that from the number of control, the rate of control, and the cost of control, ETIC has obvious advantages than CIC for uniform synchronization of master–slave Lorenz systems. • A synchronization scheme via event-triggered impulsive control (ETIC) is proposed. • The synchronization via ETIC is executed when one of state-based events is triggered. • The classic impulsive synchronization is significantly improved via ETIC. • The synchronization via ETIC is robust with respect to time-delays. • Lorenz systems are used to verify the performances of synchronization via ETIC. [ABSTRACT FROM AUTHOR]