Oscillations of complex networks

TL;DR

This paper investigates how complex networks respond to sudden disturbances, revealing that they can oscillate persistently when capacity is limited, with a theoretical estimate for the critical capacity triggering such oscillations.

Contribution

Introduces a model showing that finite-capacity networks can oscillate under perturbations and provides a theoretical estimate for the critical capacity causing oscillations.

Findings

Networks can oscillate persistently after disturbances.

A critical capacity parameter determines oscillation onset.

Oscillations imply complex networks are highly dynamic.

Abstract

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.