Partial Synchronization and Partial Amplitude Death in Mesoscale Network Motifs

TL;DR

This paper introduces an analytical method to predict complex space-time patterns, such as partial amplitude death and synchronization, in small undirected networks of Stuart-Landau oscillators based solely on network topology.

Contribution

It presents a novel approach linking network topology to pattern stability, applicable to larger networks and robust against frequency mismatches.

Findings

Partial amplitude death and synchronization are prevalent in small networks.

The method accurately predicts pattern existence from topology.

Stability of full synchronization relates to specific topological eigenvalues.

Abstract

We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based solely on the network topology. These patterns consist of partial amplitude death and partial synchronization and are found to exist in large variety for all undirected networks of up to 5 nodes. The underlying concept is proved to be robust with respect to frequency mismatch and can also be extended to larger networks. In addition it directly links the stability of complete in-phase synchronization to only a small subset of topological eigenvalues of a network.