Abstract
A single node failure capacity control function taking into account attack strength, attack times, control node load intensity and the degree of attacked node is proposed in this paper to mitigate the cascading failure of complex networks under random attack. An optimal probability allocation mechanism of redundant resources is established by targeting the load of each neighbor node. Then, the node failure capacity control function and allocation mechanism are used to define the phase transition critical factor and robustness indicator that used the attack strength, control node load intensity and the degree of attacked node as the parameters. Based on the above analysis, the phase transition critical factor model of degree distribution of scale-free network and random network is derived, and the dynamic change law between the parameters and phase transition critical state as well as robust performance of classical network and real network is analyzed. The theoretical and experimental results show that in the controllable region, the smaller the degree of attacked node, the greater the control node load intensity and the more difficult the phase transition critical state to be achieved, and the better the effect of mitigating cascading failure. Besides, the robustness of the network with cascading failure is mutually affected by the control node load capacity, the degree of attacked node and phase transition critical factor within a certain range, which thus embarks on a new perspective to mitigate the failure.
Highlights
Almost all infrastructure networks in the real world can be regarded as complex networks, such as power grid [1]–[5], communication network [6], transportation network [7]–[9] and the Internet [10], etc., in which there are a large number of nodes connecting to each other as well as links transmitting information and energy
The cascading failure models of classical and actual networks under the external random attack are constructed based on the optimal probability distribution mechanism of neighbor node load and the node failure capacity control function, and through controlling the changes of important parameters in the model, the corresponding indexes are used to analyze the cascading failure mechanism of each node of the network and their influence on some characteristics of cascading failure model
1) Theoretical analysis and simulation results show that the analytic evolution model of node failure constructed based on two classical networks and two actual networks as well as the cascading failure model based on the optimal probability allocation mechanism are reasonable, which has provided a theoretical basis for the study of the cascading failure mechanism and the making of mitigation strategies of complex networks in real world
Summary
Almost all infrastructure networks in the real world can be regarded as complex networks, such as power grid [1]–[5], communication network [6], transportation network [7]–[9] and the Internet [10], etc., in which there are a large number of nodes connecting to each other as well as links transmitting information and energy. As the information transfer station with storage capacity in the network, the node load is inevitably attacked by the external world during the operation, causing a series of dynamic losses in a network, i.e. cascading failure of complex networks [11]–[13]. The external world, some nodes become invalid in the target network, which leads to the redistribution of the node load and the loss of input-output ability of some redistributed node load due to exceeding the load capacity. The failure of these nodes may cause the failure of other nodes through the redistribution.
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