Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time series data

TL;DR

This paper introduces a data-driven method to estimate phase and amplitude functions of limit-cycle oscillators from time series data, enabling applications like fast entrainment and amplitude control without prior model knowledge.

Contribution

The authors develop a polynomial regression-based estimation method for phase and amplitude functions that is formulated as a convex optimization problem, applicable to observed time series data.

Findings

The method accurately estimates phase and amplitude functions in numerical examples.

It enables data-driven fast entrainment with amplitude suppression.

The approach does not require prior knowledge of the oscillator's dynamical equations.

Abstract

We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial regression and can be solved as a convex optimization problem. The validity of the proposed method is numerically illustrated by using two-dimensional limit-cycle oscillators as examples. As an application, we demonstrate data-driven fast entrainment with amplitude suppression using the optimal periodic input derived from the estimated phase and amplitude functions.