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arXiv · 1905.10133

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

Irina V. Tyulkina·Denis S. Goldobin·Arkady Pikovsky
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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.

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Irina V. Tyulkina, Denis S. Goldobin, Arkady Pikovsky. 2019-05-24. Stabilization of direct numerical simulation for finite truncations of circular cumulant expansions. https://doi.org/10.1088/1757-899x%2F581%2F1%2F012008

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