Time scale modeling of sparse dynamic networks

This paper develops a time-scale approach to the decomposition and aggregation of dynamic networks with dense and sparse connections. Two parameters are used to characterize time-scale and weak coupling properties. Bounds in terms of these parameters determine when there are two time-scales in sparse networks. Simplified models of the slow and fast subsystems are proposed and physical interpretations are provided. The results are illustrated with a 2000-node power network.