Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise

• Published in: arXiv.org
• Main Authors: Tönjes, Ralf, Pikovsky, Arkady
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 10.09.2020
• Subjects: Order parameters; Oscillators; Physics - Adaptation and Self-Organizing Systems; Physics - Disordered Systems and Neural Networks
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2009.04725

We study an ensembles of globally coupled or forced identical phase oscillators subject to independent white Cauchy noise. We demonstrate, that if the oscillators are forced in several harmonics, stationary synchronous regimes can be exactly described with a finite number of complex order parameters. The corresponding distribution of phases is a product of wrapped Cauchy distributions. For sinusoidal forcing, the Ott-Antonsen low-dimensional reduction is recovered.