Stabilization of direct numerical simulation for finite truncations of circular cumulant expansions
arXiv:1905.10133 · doi:10.1088/1757-899X/581/1/012008
Abstract
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.
arXiv comment8 pages, 7 figures
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