Dynamical Motifs: Building Blocks of Complex Network Dynamics

TL;DR

This paper introduces dynamical motifs as fundamental building blocks to understand complex network dynamics, revealing how their presence explains transitions from quiescence to chaos or periodicity in neural networks.

Contribution

It proposes a novel framework analyzing small subnetworks with specific dynamics to explain large-scale network behavior.

Findings

Transition from quiescence to chaos with increasing connection density

Periodic dynamics dominate in spatially distributed networks

Dynamical motifs correlate with observed network behaviors

Abstract

Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and chaotic dynamics. We simulate randomly connected neural networks and, with increasing density of connections, observe the transition from quiescence to periodic and chaotic dynamics. We explain this transition by the appearance of dynamical motifs in the structure of these networks. We also observe domination of periodic dynamics in simulations of spatially distributed networks with local connectivity and explain it by absence of chaotic and presence of periodic motifs in their structure.