Uni-directional synchronization and frequency difference locking induced by a heteroclinic ratchet

TL;DR

This paper investigates a system of four coupled oscillators that demonstrates unique uni-directional synchronization and frequency locking phenomena caused by a heteroclinic ratchet, especially under the influence of noise.

Contribution

It introduces the concept of a heteroclinic ratchet in coupled oscillators and analyzes its role in uni-directional synchronization and frequency locking effects.

Findings

Existence of a heteroclinic ratchet causes uni-directional synchronization.

Frequency difference locking occurs with added white noise.

Unusual synchronization phenomena are demonstrated in the oscillator system.

Abstract

A system of four coupled oscillators that exhibits unusual synchronization phenomena has been ana- lyzed. Existence of a one-way heteroclinic network, called heteroclinic ratchet, gives rise to uni-directional (de)synchronization between certain groups of cells. Moreover, we show that locking in frequency differ- ences occur when a small white noise is added to the dynamics of oscillators.