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

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.

11 pages, 4figures

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Cited by in corpus (2)

• Macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian white noise
• Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise