Local complexity predicts global synchronization of hierarchically networked oscillators

TL;DR

This paper investigates how local complexity in hierarchically-organized oscillator networks influences their global synchronization, revealing that local attractor structures can control overall network synchrony.

Contribution

It introduces a model of hierarchical Stuart-Landau oscillators with activity-dependent couplings and shows how local motif structures affect global synchronization patterns.

Findings

Local attractor number correlates with synchronization.

Anti-symmetric motifs generate diverse attractors.

Local complexity enables control of global synchronization.

Abstract

We study the global synchronization of hierarchically-organized Stuart-Landau oscillators, where each subsystem consists of three oscillators with activity-dependent couplings. We consider all possible coupling signs between the three oscillators, and find that they can generate different numbers of phase attractors depending on the network motif. Here, the subsystems are coupled through mean activities of total oscillators. Under weak inter-subsystem couplings, we demonstrate that the synchronization between subsystems is highly correlated with the number of attractors in uncoupled subsystems. Among the network motifs, perfect anti-symmetric ones are unique to generate both single and multiple attractors depending on the activities of oscillators. The flexible local complexity can make global synchronization controllable.