Stabilization of direct numerical simulation for finite truncations of circular cumulant expansions

21st Winter School on Continuous Media Mechanics

计算机技术

Tyulkina, I.V.^1^2 ; Goldobin, D.S.^1^2 ; Pikovsky, A.^3^4

Institute of Continuous Media Mechanics UB RAS, 1 Akademika Koroleva street, Perm

614013, Russia^1

Department of Theoretical Physics, Perm State University, 15 Bukireva street, Perm

614990, Russia^2

Institute for Physics and Astronomy, University of Potsdam, 24/25 Karl-Liebknecht-Strasse, Potsdam

14476, Germany^3

Department of Control Theory, Nizhny Novgorod State University, 23 Gagarin Avenue, Nizhny Novgorod

606950, Russia^4

关键词: Coupled oscillators;    Cumulant expansion;    Cumulants;    Direct simulation;    Natural systems;    Numerical instability;    Stabilization techniques;    Truncated equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/581/1/012008/pdf
DOI  :  10.1088/1757-899X/581/1/012008

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

We study a numerical instability of direct simulations with truncated equation chains for the "circular cumulant" representation and two approaches to its suppression. The approaches are tested for a chimera-bearing hierarchical population of coupled oscillators. The stabilization techniques can be efficiently applied without significant effect on the natural system dynamics within a finite vicinity of the Ott-Antonsen manifold for direct numerical simulations with up to 20 cumulants; with increasing deviation from the Ott-Antonsen manifold the stabilization becomes more problematic.