Oscillations of complex networks

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 quantities respond to sudden changes caused by attacks or disturbances in recoverable networks, i.e., functions of the affected nodes are only temporarily disabled or partially limited. By introducing a model to address this issue, we find that, for a finite-capacity network, perturbations can cause the network to 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.