On controlling networks of limit-cycle oscillators

TL;DR

This paper develops control methods for network-coupled limit-cycle oscillators to achieve complete frequency synchronization with minimal control interventions, extending previous phase oscillator work.

Contribution

It introduces two control strategies for limit-cycle oscillators, focusing on stabilization and synchronization, with numerical demonstrations and analysis of potential failures.

Findings

Control can synchronize oscillators with minimal interventions

Two control types differ in amplitude targeting

Numerical examples validate the methods

Abstract

The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here we study the control of network-coupled limit cycle oscillators, extending previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of control. The first type directs oscillators towards to larger amplitudes, while the second does not. We present numerical examples of both control types and comment on the potential failures of the method.