Synchronization of higher-dimensional Kuramoto oscillators on networks: from scalar to matrix-weighted couplings (opens in new tab)

arXiv:2603.08352v1 Announce Type: new Abstract: The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each characterized by a scalar phase and a natural frequency, by interacting through a sinusoidal coupling. In this work, we propose a d-dimensional generalization in which oscillators are represented as unit vectors on the (d-1)-sphere and interact through a matrix-weighted ...