Does dynamics reflect topology in directed networks?

TL;DR

This paper investigates how the topology of directed networks influences their dynamics, identifying a transition from order to disorder and developing a method to predict disordered dynamics based on network structure.

Contribution

It introduces a topologically induced transition in directed oscillator networks and proposes a novel method to predict disordered dynamics from network topology.

Findings

Transition from synchronized to disordered dynamics identified

Disordered dynamics are precisely determined by network topology

Method developed to predict dynamics from topology

Abstract

We present and analyze a topologically induced transition from ordered, synchronized to disordered dynamics in directed networks of oscillators. The analysis reveals where in the space of networks this transition occurs and its underlying mechanisms. If disordered, the dynamics of the units is precisely determined by the topology of the network and thus characteristic for it. We develop a method to predict the disordered dynamics from topology. The results suggest a new route towards understanding how the precise dynamics of the units of a directed network may encode information about its topology.