Time-delay robustness of consensus problems in regular and complex networks

Recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. Based on the theory of complex networks and computer simulation, we analyze the robustness to time-delay in linear consensus problem with different network topologies, such as global coupled network, star network, nearest-neighbor coupled network, small-world network, and scale-free network. It is found that global coupled network, star network, and scale-free network are vulnerable to time-delay, while nearest-neighbor coupled network and small-world network are robust to time-delay. And it is found that the maximum node degree of the network is a good predictor for time-delay robustness. And it is found that the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges in scale-free network.