Goldobin Denis S, Tyulkina Irina V, Klimenko Lyudmila S, Pikovsky Arkady
Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, 614013 Perm, Russia.
Department of Theoretical Physics, Perm State University, Bukirev Street 15, 614990 Perm, Russia.
Chaos. 2018 Oct;28(10):101101. doi: 10.1063/1.5053576.
We analyze the accuracy of different low-dimensional reductions of the collective dynamics in large populations of coupled phase oscillators with intrinsic noise. Three approximations are considered: (i) the Ott-Antonsen ansatz, (ii) the Gaussian ansatz, and (iii) a two-cumulant truncation of the circular cumulant representation of the original system's dynamics. For the latter, we suggest a closure, which makes the truncation, for small noise, a rigorous first-order correction to the Ott-Antonsen ansatz, and simultaneously is a generalization of the Gaussian ansatz. The Kuramoto model with intrinsic noise and the population of identical noisy active rotators in excitable states with the Kuramoto-type coupling are considered as examples to test the validity of these approximations. For all considered cases, the Gaussian ansatz is found to be more accurate than the Ott-Antonsen one for high-synchrony states only. The two-cumulant approximation is always superior to both other approximations.
我们分析了具有内在噪声的大量耦合相位振子集体动力学的不同低维约简的准确性。考虑了三种近似方法：（i）奥-安唐斯近似，（ii）高斯近似，以及（iii）对原系统动力学的循环累积量表示进行双累积量截断。对于后者，我们提出了一种封闭形式，对于小噪声情况，该截断是对奥-安唐斯近似的严格一阶修正，同时也是高斯近似的推广。以内在噪声的库拉托莫模型以及具有库拉托莫型耦合的处于可激发状态的相同噪声有源转子群体为例，来检验这些近似方法的有效性。对于所有考虑的情况，发现高斯近似仅在高同步状态下比奥-安唐斯近似更准确。双累积量近似始终优于其他两种近似。
