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

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.

13 pages, 11 figures

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Cited by in corpus (7)

• Designing two-dimensional limit-cycle oscillators with prescribed trajectories and phase-response characteristics
• Optimal coupling functions for fast and global synchronization of weakly coupled limit-cycle oscillators
• Setting of the Poincaré section for accurately calculating the phase of rhythmic spatiotemporal dynamics
• Phase autoencoder for rapid data-driven synchronization of rhythmic spatiotemporal patterns
• Gaussian Process Phase Interpolation for estimating the asymptotic phase of a limit cycle oscillator from time series data
• Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators
• Distinguishing pairwise and higher-order interactions in coupled oscillators from time series