Two-dimensional hydrodynamic simulation for synchronization in coupled density oscillators

TL;DR

This paper uses 2D hydrodynamic simulations and phase reduction theory to analyze synchronization phenomena in coupled density oscillators, revealing stable anti-phase, three-phase, and partial-in-phase states.

Contribution

It introduces a hydrodynamic simulation approach combined with phase reduction analysis to study synchronization in coupled density oscillators, identifying various stable synchronization modes.

Findings

Stable anti-phase, three-phase, and partial-in-phase synchronization modes identified.

Synchronization modes depend on the number of coupled oscillators.

Phase coupling function's Fourier component explains phase dynamics.

Abstract

A density oscillator is a fluid system in which oscillatory flow occurs between different density fluids through the pore connecting them. We investigate the synchronization in coupled density oscillators using two-dimensional hydrodynamic simulation and analyze the stability of the synchronous state based on the phase reduction theory. Our results show that the anti-phase, three-phase, and 2-2 partial-in-phase synchronization modes spontaneously appear as stable states in two, three, and four coupled oscillators, respectively. The phase dynamics of coupled density oscillators is interpreted with their sufficiently large first Fourier components of the phase coupling function.