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arXiv · 1810.11213

Relationships between the Distribution of Watanabe-Strogatz Variables and Circular Cumulants for Ensembles of Phase Elements

Denis S. Goldobin
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Abstract

The Watanabe-Strogatz and Ott-Antonsen theories provided a seminal framework for rigorous and comprehensive studies of collective phenomena in a broad class of paradigmatic models for ensembles of coupled oscillators. Recently, a "circular cumulant" approach was suggested for constructing the perturbation theory for the Ott-Antonsen approach. In this paper, we derive the relations between the distribution of Watanabe-Strogatz phases and the circular cumulants of the original phases. These relations are important for the interpretation of the circular cumulant approach in the context of the Watanabe-Strogatz and Ott-Antonsen theories. Special attention is paid to the case of hierarchy of circular cumulants, which is generally relevant for constructing perturbation theories for the Watanabe-Strogatz and Ott-Antonsen approaches.

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BibTeXRIS

Denis S. Goldobin. 2018-10-26. Relationships between the Distribution of Watanabe-Strogatz Variables and Circular Cumulants for Ensembles of Phase Elements. https://doi.org/10.1142/s0219477519400029

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