Synchronization Patterns: From Network Motifs to Hierarchical Networks

TL;DR

This paper explores how hierarchical and fractal network topologies influence complex synchronization patterns in coupled oscillators, revealing new insights into the relationship between network structure and dynamics, including the induction of oscillation death.

Contribution

It introduces an analytical eigensolution method to predict dynamics in large hierarchical networks from small motifs, and demonstrates the emergence of oscillation death in symmetric coupling networks.

Findings

Hierarchical networks exhibit corresponding hierarchical dynamics.

Oscillation death can occur even with symmetric coupling.

The eigensolution method predicts large network behavior from small motifs.

Abstract

We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is motivated by the network of neurons in the brain. This fractal property is well represented in hierarchical networks, for which we present three different models. In addition, we introduce an analytical eigensolution method and provide a comprehensive picture of the interplay of network topology and the corresponding network dynamics, thus allowing us to predict the dynamics of arbitrarily large hierarchical networks simply by analyzing small network motifs. We also show that oscillation death can be induced in these networks, even if the coupling is symmetric, contrary to previous understanding of oscillation death. Our results show that there is a direct correlation between topology and dynamics: Hierarchical networks exhibit the corresponding hierarchical dynamics. This helps bridging the gap between mesoscale motifs and macroscopic networks.