Anti-phase synchronization of phase-reduced oscillators using open-loop control

TL;DR

This paper demonstrates a method to achieve and sustain anti-phase synchronization between two nonlinear oscillators with different natural frequencies using open-loop control with square pulses, showing feedback is not always necessary.

Contribution

It introduces an open-loop control technique employing square pulses to induce anti-phase synchronization in nonlinear oscillators, expanding control options without feedback.

Findings

Open-loop control can effectively induce anti-phase synchronization.

Square pulse sequences are sufficient for maintaining desired oscillator states.

The method works despite differences in natural frequencies.

Abstract

In this letter, we present an elegant method to build and maintain an anti-phase configuration of two nonlinear oscillators with different natural frequencies and dynamics described by the sinusoidal phase-reduced model. The anti-phase synchronization is achieved using a common input that couples the oscillators and consists of a sequence of square pulses of appropriate amplitude and duration. This example provides a proof of principle that open-loop control can be used to create desired synchronization patterns for nonlinear oscillators, when feedback is expensive or impossible to obtain.