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arXiv · 2305.18027

Circular cumulant reductions for macroscopic dynamics of oscillator populations with non-Gaussian noise

Anastasiya V. Dolmatova·Irina V. Tyulkina·Denis S. Goldobin
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Abstract

We employ the circular cumulant approach to construct a low dimensional description of the macroscopic dynamics of populations of phase oscillators (elements) subject to non-Gaussian white noise. Two-cumulant reduction equations for alpha-stable noises are derived. The implementation of the approach is demonstrated for the case of the Kuramoto ensemble with non-Gaussian noise. The results of direct numerical simulation of the ensemble of N=1500 oscillators and the "exact" numeric solution for the fractional Fokker-Planck equation in the Fourier space are found to be in good agreement with the analytical solutions for two feasible circular cumulant model reductions. We also illustrate that the two-cumulant model reduction is useful for studying the bifurcations of chimera states in hierarchical populations of coupled noisy phase oscillators.

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Anastasiya V. Dolmatova, Irina V. Tyulkina, Denis S. Goldobin. 2023-05-29. Circular cumulant reductions for macroscopic dynamics of oscillator populations with non-Gaussian noise. https://doi.org/10.1063/5.0159982

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