Phase autoencoder for limit-cycle oscillators
This work addresses a fundamental challenge in analyzing synchronization dynamics for researchers in nonlinear systems and oscillator theory, though it is incremental as it builds on existing autoencoder methods.
The authors tackled the problem of estimating the asymptotic phase and phase sensitivity function of limit-cycle oscillators without relying on mathematical models, by developing a phase autoencoder trained on time-series data, which successfully performed these estimations and enabled global synchronization of oscillators.
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.