Controlling synchrony by delay coupling in networks: from in-phase to splay and cluster states

TL;DR

This paper investigates how delay coupling and phase tuning in oscillator networks can control synchronization states, enabling transitions between in-phase, splay, and cluster states with robustness to element nonidentity.

Contribution

It introduces the coupling phase as a key control parameter for switching synchronization states in delay-coupled oscillator networks, supported by analytical stability conditions.

Findings

Coupling phase controls stability of synchronous states

Switching between in-phase, cluster, and splay states demonstrated

Robustness of control to nonidentical network elements

Abstract

We study synchronization in delay-coupled oscillator networks, using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of super- or subcritical Hopf bifurcation) we derive analytical stability conditions and demonstrate that by tuning the coupling phase one can easily control the stability of synchronous periodic states. We propose the coupling phase as a crucial control parameter to switch between in-phase synchronization or desynchronization for general network topologies, or between in-phase, cluster, or splay states in unidirectional rings. Our results are robust even for slightly nonidentical elements of the network.