Stabilizing Stuart-Landau oscillators via time-varying networks

TL;DR

This paper presents a method to stabilize synchronization in Stuart-Landau oscillators by dynamically switching between two networks, using network plasticity and analytical criteria for optimal switching rates.

Contribution

It introduces a novel approach to enforce synchronization through time-varying networks and provides an analytical framework for the switching rate required.

Findings

Synchronization can be restored by network switching at a critical rate.

The method is rigorously supported by the average theorem.

Engineered networks enable control of oscillator dynamics.

Abstract

A procedure is developed and tested to enforce synchronicity in a family of Stuart-Landau oscillators, coupled through a symmetric network. The proposed method exploits network plasticity, as an inherent non autonomous drive. More specifically, we assume that the system is initially confined on a network which turns the underlying homogeneous synchronous state unstable. A properly engineered network can be always generated, which links the same set of nodes, and allows for synchronicity to be eventually restored, upon performing continuously swappings, at a sufficient rate, between the two aforementioned networks. The result is cast in rigorous terms, as follows an application of the average theorem and the critical swapping rate determined analytically.