Open AccessDescription of the macroscopic dynamics of populations of phase elements with white non-Gaussian noise based on the circular cumulant approach
Author(s) -
А. В. Долматова,
I. V. Tiulkina,
Denis S. Goldobin
Publication year - 2021
Publication title -
vestnik permskogo universiteta. seriâ, fizika
Language(s) - English
Resource type - Journals
ISSN - 1994-3598
DOI - 10.17072/1994-3598-2021-3-05-12
Subject(s) - cumulant , white noise , statistical physics , gaussian , gaussian noise , noise (video) , mathematics , limit (mathematics) , additive white gaussian noise , physics , mathematical analysis , statistics , quantum mechanics , algorithm , computer science , artificial intelligence , image (mathematics)
We use the method of circular cumulants, which allows us to construct a low-mode macroscopic description of the dynamics of populations of phase elements subject to non-Gaussian white noise. In this work, we have obtained two-cumulant reduced equations for alpha-stable noise. The application of the approach is demonstrated for the case of the Kuramoto ensemble with non-Gaussian noise. The results of numerical calculations for the ensemble of N = 1500 elements, the numericalsimulation of the chain of equations for the Kuramoto–Daido order parameters (Fourier modes of the probability density) with 200 terms (in the thermodynamic limit of an infinitely large ensemble) and the theoretical solution on the basis of the two-cumulant approximation are in good agreement with each other.