Definition and data-driven reconstruction of asymptotic phase and amplitudes of stochastic oscillators via Koopman operator theory

TL;DR

This paper introduces a data-driven method using Koopman operator theory and EDMD to estimate asymptotic phase and amplitudes of stochastic oscillators from time-series data, demonstrated on a neuron model.

Contribution

It extends the concept of asymptotic phase and amplitude to stochastic systems and applies EDMD for their data-driven reconstruction.

Findings

Successfully reconstructed phase and amplitude functions from noisy data

Extended Koopman analysis applied to stochastic oscillators

Demonstrated on FitzHugh-Nagumo neuron model

Abstract

Asymptotic phase and amplitudes are fundamental concepts in the analysis of limit-cycle oscillators. In this paper, we briefly review the definition of these quantities, particularly a generalization to stochastic oscillatory systems from the viewpoint of Koopman operator theory, and discuss a data-driven approach to estimate the asymptotic phase and amplitude functions from time-series data of stochastic oscillatory systems. We demonstrate that the standard Extended dynamic mode decomposition (EDMD) can successfully reconstruct the phase and amplitude functions of the noisy FitzHugh-Nagumo neuron model only from the time-series data.