Inferring Coupled Stuart-Landau Equations from Waveforms

TL;DR

This paper introduces a data-driven method to infer coupled Stuart-Landau equations from waveform data, enabling analysis of synchronization and bifurcations in oscillatory systems.

Contribution

The authors develop a novel framework to reconstruct phase-amplitude models directly from waveform measurements, applicable to high-dimensional systems.

Findings

Accurately recovers parameters for coupled van der Pol oscillators.

Captures bistability and synchronization transitions in hydrodynamic oscillators.

Reveals bifurcation mechanisms destabilizing anti-phase states.

Abstract

We present a data-driven framework to infer phase-amplitude equations of coupled limit-cycle oscillators directly from waveform measurements. Exploiting the universality of the Stuart-Landau normal form near a supercritical Hopf bifurcation, we reconstruct a near-identity transformation from two independent observables of an isolated oscillator and infer the intrinsic Stuart-Landau parameters. Using this reconstructed transformation, we then estimate linear coupling coefficients from paired measurements. The method accurately recovers parameters for coupled van der Pol oscillators, providing a quantitative benchmark. Applied to a high-dimensional hydrodynamic system of two coupled collapsible-channel oscillators, the inferred Stuart-Landau model captures bistability between in-phase and anti-phase synchronization and reveals that the anti-phase state is destabilized through a Neimark-Sacker bifurcation. Our approach enables quantitative prediction of synchronization transitions involving amplitude dynamics from experimentally accessible waveform data.