Research on proactive defense and dynamic repair of complex networks considering cascading effects.

Cascading effects can result in the nonlinear propagation of failures in complex networks, ultimately leading to network collapse. Research on the fault propagation principles, defense strategies, and repair strategies can help mitigate the effects of cascading failures. Especially, proactive defense and dynamic repair are flexible and effective methods to ensure network security. Most studies on the cascade of complex networks are based on the unprocessed initial information of the network. However, marginal nodes are a type of node that cloaks the initial information of the network. In this study, we rank the importance of nodes according to the intensity of network energy confusion after the removal of this node, clarify the meaning of marginal nodes and proposed two methods to screen marginal nodes. The results indicated that the proactive removal of marginal nodes can effectively reduce the effect of cascading failures without causing any negative disturbance to the energy flow of the network. In addition, network repair according to the proposed strategy can minimize the cascade effect in the repair process and improve repair efficiency.

Multivariate recovery coupling in interdependent networks with cascading failure.

Interdependent networks are susceptible to catastrophic consequences due to the interdependence between the interacting subnetworks, making an effective recovery measure particularly crucial. Empirical evidence indicates that repairing the failed network component requires resources typically supplied by all subnetworks, which imposes the multivariate dependence on the recovery measures. In this paper, we develop a multivariate recovery coupling model for interdependent networks based on percolation theory. Considering the coupling structure and the failure-recovery relationship, we propose three recovery strategies for different scenarios based on the local stability of nodes. We find that the supporting network plays a more important role in improving network resilience than the network where the repaired component is located. This is because the recovery strategy based on the local stability of the supporting nodes is more likely to obtain direct benefits. In addition, the results show that the average degree and the degree exponent of the networks have little effect on the superior performance of the proposed recovery strategies. We also find a percolation phase transition from first to second order, which is strongly related to the dependence coefficient. This indicates that the more the recovery capacity of a system depends on the system itself, the more likely it is to undergo an abrupt transition under the multivariate recovery coupling. This paper provides a general theoretical frame to address the multivariate recovery coupling, which will enable us to design more resilient networks against cascading failures.

Percolation transitions in interdependent networks with reinforced dependency links.

Dependence can highly increase the vulnerability of interdependent networks under cascading failure. Recent studies have shown that a constant density of reinforced nodes can prevent catastrophic network collapses. However, the effect of reinforcing dependency links in interdependent networks has rarely been addressed. Here, we develop a percolation model for studying interdependent networks by introducing a fraction of reinforced dependency links. We find that there is a minimum fraction of dependency links that need to be reinforced to prevent the network from abrupt transition, and it can serve as the boundary value to distinguish between the first- and second-order phase transitions of the network. We give both analytical and numerical solutions to the minimum fraction of reinforced dependency links for random and scale-free networks. Interestingly, it is found that the upper bound of this fraction is a constant 0.088 01 for two interdependent random networks regardless of the average degree. In particular, we find that the proposed method has higher reinforcement efficiency compared to the node-reinforced method, and its superiority in scale-free networks becomes more obvious as the coupling strength increases. Moreover, the heterogeneity of the network structure profoundly affects the reinforcement efficiency. These findings may provide several useful suggestions for designing more resilient interdependent networks.

Effect of load-capacity heterogeneity on cascading overloads in networks.

Heterogeneity in the load capacity of nodes is a common characteristic of many real-world networks that can dramatically affect their robustness to cascading overloads. However, most studies seeking to model cascading failures have ignored variations in nodal load capacity and functionality. The present study addresses this issue by extending the local load redistribution model to include heterogeneity in nodal load capacity and heterogeneity in the types of nodes employed in the network configuration and exploring how these variations affect network robustness. Theoretical and numerical analyses demonstrate that the extent of cascading failure is influenced by heterogeneity in nodal load capacity, while it is relatively insensitive to heterogeneity in nodal configuration. Moreover, the probability of cascading failure initiation at the critical state increases as the range of nodal load capacities increases. However, for large-scale networks with degree heterogeneity, a wide range of nodal load capacities can also suppress the spread of failure after its initiation. In addition, the analysis demonstrates that heterogeneity in nodal load capacity increases and decreases the extent of cascading failures in networks with sublinear and superlinear load distributions, respectively. These findings may provide some practical implications for controlling the spread of cascading failure.