The local-world (LW) evolving network model shows a transition for the degree distribution between the exponential and power-law distributions, depending on the LW size. Cascading failures under intentional attacks in LW network models with different LW sizes were investigated using the cascading failures load model. We found that the LW size has a significant impact on the network's robustness against deliberate attacks. It is much easier to trigger cascading failures in LW evolving networks with a larger LW size. Therefore, to avoid cascading failures in real networks with local preferential attachment such as the Internet, the World Trade Web and the multi-agent system, the LW size should be as small as possible.
An adaptive predictive pinning control is proposed to suppress the cascade in coupled map lattices (CMLs).Two monitoring strategies are applied:(1) A specific fraction of nodes with the highest degree or betweenness are chosen to constitute the set of monitored nodes;(2) During the cascade,an adaptive pinning control is implemented,in which only the nodes in the monitored set whose current state is normal but whose predictive state is abnormal,are pinned with the predictive controller.Simulations show that for the scale-free (SF) CML the degree-based monitoring strategy is advantageous over the betweenness-based strategy,while for the small-world (SW) CML the situation is the opposite.With the adaptive predictive pinning control,the fewer local controllers can effectively suppress the cascade throughout the whole network.
