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Register a new userRelationships between the Distribution of Watanabe-Strogatz Variables and Circular Cumulants for Ensembles of Phase Elements
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Authors
Denis S. Goldobin
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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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