Multiple dynamical time-scales in networks with hierarchically nested modular organization

TL;DR

This paper demonstrates that hierarchical modular networks inherently produce multiple distinct dynamical time-scales, which may facilitate the separation of processes at different spatial levels in natural systems.

Contribution

It introduces a simple hierarchical modular network model showing how topological structure induces multiple characteristic dynamical time-scales.

Findings

Hierarchical modularity leads to multiple time-scale separation.

Synchronization dynamics exhibit as many time-scales as hierarchical levels.

Hierarchical organization may serve functional roles in natural systems.

Abstract

Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical levels, where the clusters defined at one level appear as elementary entities at the next higher level. Using a simple model of a hierarchical modular network, we show that such a topological structure gives rise to characteristic time-scale separation between dynamics occurring at different levels of the hierarchy. This generalizes our earlier result for simple modular networks, where fast intra-modular and slow inter-modular processes were clearly distinguished. Investigating the process of synchronization of oscillators in a hierarchical modular network, we show the existence of as many distinct time-scales as there are hierarchical levels in the system. This suggests a possible functional role of such mesoscopic organization principle in natural systems, viz., in the dynamical separation of events occurring at different spatial scales.