Heteroclinic Ratchets in a System of Four Coupled Oscillators

TL;DR

This paper investigates a unique dynamical phenomenon called heteroclinic ratchets in a system of four coupled oscillators, revealing how specific detunings lead to asymmetric phase locking behavior due to heteroclinic networks.

Contribution

It introduces the concept of heteroclinic ratchets in coupled oscillators and analyzes their robustness and response to detuning, expanding understanding of complex oscillator dynamics.

Findings

Robust heteroclinic ratchet attractors exist in the system.

Phase locking breaks asymmetrically depending on the sign of detuning.

Heteroclinic networks underpin the observed dynamical behavior.

Abstract

We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. We show that the system can have a robust attractor that responds to a specific detuning between certain pairs of the oscillators by a breaking of phase locking for arbitrary positive detunings but not for negative detunings. As the dynamical mechanism behind this is a particular type of heteroclinic network, we call this a 'heteroclinic ratchet' because of its dynamical resemblance to a mechanical ratchet.