Cascading failures in coupled map lattices with sustained attack

Many realistic networked systems may face sustained attack over a sequence of time. In this paper, we propose a cascading failure model in coupled map lattices (CMLs) with sustained attack, where a number of crucial nodes will be attacked one by one at each time step. The effects of four attacking strategies: high-degree strategy (HDS), high-clustering coefficient strategy, high-closeness strategy and high-betweenness strategy are compared. This shows that the performance of HDS is better than that of other attacking strategies when the value of the outside attack is small. The effectiveness of HDS on Watts–Strogatz (WS) small-world networks and two real-world networks is extensively investigated. The results indicate that increasing the value of the rewiring probability of WS networks can make the network more robust to resist sustained attack. The sparser the network structure is, the faster the diffusion velocity of cascading failures is. A smaller coupling strength in CMLs can restrain the diffusion velocity of cascades. We also extend our CML-based model with sustained attack from one node strategy (ONS) to two nodes strategy (TNS) and compare the effect of ONS and TNS with different values of the outside attack. It is found that ONS outperforms TNS for small values of the outside attack, but TNS would be a better choice when the outside attack and the time step are all large. Our work will provide new insights into the problem of protecting complex networks against cascading failures with respect to malicious attack.