Year: 2026
Type: preprint
Abstract: Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It is also used in power system control. The simplest possible model assumes that all oscillators are identical and connected to each other with equal pairwise attraction. In this paper, we give a full geometric description of its global dynamics in terms of Morse theory and dynamical systems. Most of this description is stable in the sense that it is topologically preserved under small perturbations of the parameters.
Source: arXiv (Cornell University)
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162296009