Phase autoencoder for limit-cycle oscillators

TL;DR

This paper introduces a phase autoencoder that learns to encode the asymptotic phase of limit-cycle oscillators from data, enabling phase estimation, sensitivity analysis, and synchronization without explicit mathematical models.

Contribution

The paper presents a novel autoencoder approach that directly encodes the asymptotic phase of oscillators from time-series data, facilitating model-free analysis and synchronization.

Findings

Accurately estimates asymptotic phase from data

Reconstructs oscillator states on the limit cycle

Enables global synchronization of oscillators

Abstract

We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.