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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Ott-Antonsen ansatz for the D-dimensional Kuramoto model: A constructive approach

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Barioni, Ana Elisa D. [1] ; de Aguiar, Marcus A. M. [1]
Total Authors: 2
[1] Univ Estadual Campinas, UNICAMP, Inst Fis Gleb Wataghin, BR-13083970 Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Chaos; v. 31, n. 11 NOV 2021.
Web of Science Citations: 0

Kuramoto's original model describes the dynamics and synchronization behavior of a set of interacting oscillators represented by their phases. The system can also be pictured as a set of particles moving on a circle in two dimensions, which allows a direct generalization to particles moving on the surface of higher dimensional spheres. One of the key features of the 2D system is the presence of a continuous phase transition to synchronization as the coupling intensity increases. Ott and Antonsen proposed an ansatz for the distribution of oscillators that allowed them to describe the dynamics of the order parameter with a single differential equation. A similar ansatz was later proposed for the D-dimensional model by using the same functional form of the 2D ansatz and adjusting its parameters. In this article, we develop a constructive method to find the ansatz, similarly to the procedure used in 2D. The method is based on our previous work for the 3D Kuramoto model where the ansatz was constructed using the spherical harmonics decomposition of the distribution function. In the case of motion in a D-dimensional sphere, the ansatz is based on the hyperspherical harmonics decomposition. Our result differs from the previously proposed ansatz and provides a simpler and more direct connection between the order parameter and the ansatz. (AU)

FAPESP's process: 16/01343-7 - ICTP South American Institute for Fundamental Research: a regional center for theoretical physics
Grantee:Nathan Jacob Berkovits
Support Opportunities: Special Projects
FAPESP's process: 19/20271-5 - Evolutionary models in population dynamics
Grantee:Marcus Aloizio Martinez de Aguiar
Support Opportunities: Regular Research Grants
FAPESP's process: 19/24068-0 - Generalized Kuramoto oscillators with external forces
Grantee:Ana Elisa Dellamatrice Barioni
Support Opportunities: Scholarships in Brazil - Master