Applicability of the Ott–Antonsen ansatz to more complex stochastic oscillator models

Determine the validity of the Ott–Antonsen low-dimensional ansatz for stochastic, globally coupled oscillator systems beyond the standard Kuramoto setup, including models with more complex coupling functions and frequency distributions, particularly outside the small-noise regime. Establish clear conditions under which the Ott–Antonsen reduction remains accurate for these more complex oscillator models.

Background

The paper contrasts its Dean–Kawasaki plus center-manifold approach with a recent method that applies the Ott–Antonsen (OA) ansatz to derive a stochastic order-parameter equation. The OA ansatz was originally developed for deterministic dynamics and is often used under restrictive conditions that may not hold for noisy systems.

The authors highlight that while OA-based reductions can be powerful, their reliability for stochastic dynamics—and especially for models with more complicated coupling structures—has not been firmly established. This motivates a precise determination of OA’s applicability across broader classes of stochastic Kuramoto-like models.