Dolmatova Anastasiya V, Tyulkina Irina V, Goldobin Denis S
Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, 614013 Perm, Russia.
Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 603022 Nizhny Novgorod, Russia.
Chaos. 2023 Nov 1;33(11). doi: 10.1063/5.0159982.
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 α-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" numerical 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.
我们采用循环累积量方法来构建受非高斯白噪声影响的相位振荡器（元件）群体宏观动力学的低维描述。推导了α稳定噪声的双累积量约化方程。针对具有非高斯噪声的Kuramoto系综的情况，展示了该方法的实现。发现N = 1500个振荡器系综的直接数值模拟结果以及傅里叶空间中分数福克 - 普朗克方程的“精确”数值解与两个可行的循环累积量模型约化的解析解高度吻合。我们还表明，双累积量模型约化对于研究耦合噪声相位振荡器分层群体中的奇异态分岔是有用的。
