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

Autor(es)

Barioni, Ana Elisa D. ^[1] ; de Aguiar, Marcus A. M. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, UNICAMP, Inst Fis Gleb Wataghin, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Chaos; v. 31, n. 11 NOV 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 16/01343-7 - ICTP Instituto Sul-Americano para Física Fundamental: um centro regional para física teórica
• Beneficiário: Nathan Jacob Berkovits
• Modalidade de apoio: Auxílio à Pesquisa - Projetos Especiais
• Processo FAPESP: 19/20271-5 - Modelos evolutivos em dinâmica de populações
• Beneficiário: Marcus Aloizio Martinez de Aguiar
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 19/24068-0 - Osciladores generalizados de Kuramoto com forças externas
• Beneficiário: Ana Elisa Dellamatrice Barioni
• Modalidade de apoio: Bolsas no Brasil - Mestrado