Percolation of partially interdependent networks under targeted attack

Abstract

The study of interdependent networks, and in particular the robustness on networks, has attracted considerable attention. Recent studies mainly assume that the dependence is fully interdependent. However, targeted attack for partially interdependent networks simultaneously has the characteristics of generality in real world. In this letter, the comprehensive percolation of generalized framework of partially interdependent networks under targeted attack is analyzed. As $\alpha =0$ and $\alpha =1$, the percolation law is presented. Especially, when $a=b=k$, $p_1=p_2=p$, $q_A=q_B=q$, the first and second lines of phase transition coincide with each other. The corresponding phase transition diagram and the critical line between the first and the second phase transition are found. We find that the tendency of critical line is monotone decreasing with parameter $p_1$. However, for different $\alpha$, the tendency of critical line is monotone increasing with $\alpha$. In a larger sense, our findings have potential application for designing networks with strong robustness and can regulate the robustness of some current networks.

6 pages, 9 figures

References in corpus (4)

• Robustness of a Network of Networks
• Robustness of interdependent networks under targeted attack
• Cascade of failures in coupled network systems with multiple support-dependent relations
• Percolation in Interdependent and Interconnected Networks: Abrupt Change from Second to First Order Transition

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• Robustness of partially interdependent network formed of clustered networks
• Structural Robustness of Complex Networks: A Survey of A Posteriori Measures
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• $k$-core percolation on complex networks: Comparing random, localized and targeted attacks
• The robust-yet-fragile nature of interdependent networks
• Exotic Critical Behavior of Weak Multiplex Percolation
• Asymmetry in interdependence makes a multilayer system more robust against cascading failures
• Targeted Damage to Interdependent Networks
• Simultaneous first and second order percolation transitions in interdependent networks
• Cascading Failures in Networks with Proximate Dependent Nodes
• A Framework of Hierarchical Attacks to Network Controllability
• Towards a Realistic Model for Failure Propagation in Interdependent Networks
• Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review
• Percolation on networks with weak and heterogeneous dependency
• Correlated network of networks enhances robustness against catastrophic failures
• Dependency-based targeted attacks in interdependent networks
• Percolation of networks with directed dependency links
• Percolation on Networks with Antagonistic and Dependent Interactions
• Triadic percolation on multilayer networks
• Weak Multiplex Percolation