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We demonstrate the application of the circular cumulant approach forthermodynamically large populations of phase elements, where the Ott-Antonsenproperties are violated by a multiplicative intrinsic noise. The infinitecumulant equation chain is derived for the case of a sinusoidal sensitivity ofthe phase to noise. For inhomogeneous populations, a Lorentzian distribution ofnatural frequencies is adopted. Two-cumulant model reductions, which serve as ageneralization of the Ott-Antonsen ansatz, are reported. The accuracy of thesemodel reductions and the macroscopic collective dynamics of the system areexplored for the case of a Kuramototype global coupling. The Ott-Antonsenansatz and the Gaussian approximation are found to be not uniformly accuratefor non-high frequencies.

Circular Cumulant Reductions for Macroscopic Dynamics of Kuramoto Ensemble with Multiplicative Intrinsic Noise