Delayed feedback control of synchronization in weakly coupled oscillator networks

TL;DR

This paper investigates how delayed feedback control can modulate synchronization in weakly coupled oscillator networks, enabling control over phase coherence and disruption of synchronization through analytical and numerical methods.

Contribution

It derives analytical conditions for control gain and demonstrates how delayed feedback influences synchronization in oscillator networks.

Findings

Delayed feedback can induce synchronization even with weak coupling.

Control gain critically affects phase sensitivity and synchronization.

Feedback can also disrupt existing synchronized states.

Abstract

We study control of synchronization in weakly coupled oscillator networks by using a phase reduction approach. Starting from a general class of limit cycle oscillators we derive a phase model, which shows that delayed feedback control changes effective coupling strengths and effective frequencies. We derive the analytical condition for critical control gain, where the phase dynamics of the oscillator becomes extremely sensitive to any perturbations. As a result the network can attain phase synchronization even if the natural interoscillatory couplings are small. In addition, we demonstrate that delayed feedback control can disrupt the coherent phase dynamic in synchronized networks. The validity of our results is illustrated on networks of diffusively coupled Stuart--Landau and FitzHugh--Nagumo models.