A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how such a network responds to sudden changes caused by attacks or disturbances. By introducing a model to address this issue, we find that, for a finite-capacity network, perturbations can cause the network to \emph{oscillate} persistently in the sense that the characterizing quantities vary periodically or randomly with time. We provide a theoretical estimate of the critical capacity-parameter value for the onset of the network oscillation. The finding is expected to have broad implications as it suggests that complex networks may be structurally highly dynamic.
@article{arxiv.cond-mat/0607351,
title = {Oscillations of complex networks},
author = {Xingang Wang and Ying-Cheng Lai and Chong Heng Lai},
journal= {arXiv preprint arXiv:cond-mat/0607351},
year = {2009}
}