Geometric perspective of linear stability in finite networks of nonlinear oscillators
Abstract
We use a complex-valued transformation of the Kuramoto model to develop an operator-description of the linear stability in finite networks of nonlinear oscillators. This mathematical approach offers analytical predictions for the linear stability of -states, which include phase synchronization () and waves with different spatial frequencies (). This approach seamlessly incorporates the presence of time delays (represented by phase-lags in the coupling). With this, we are able to analytically determine the specific combination of connectivity and time delays (phase-lags) that leads to any given -state to be linearly stable. This approach offers a geometric perspective of linear stability in finite networks in terms of the connectivity and delays (phase-lag), and it opens a path to designing and controlling the spatiotemporal dynamics of individual oscillator networks.
Cite
@article{arxiv.2504.06377,
title = {Geometric perspective of linear stability in finite networks of nonlinear oscillators},
author = {Yashee Sinha and Priya B. Jain and Antonio Mihara and Rene O. Medrano-T and Ján Mináč and Lyle E. Muller and Roberto C. Budzinski},
journal= {arXiv preprint arXiv:2504.06377},
year = {2025}
}