Asymptotic stability of the high-dimensional Kuramoto model on Stiefel manifolds

Abstract

In this paper, we investigate the convergence properties of a heterogeneous consensus model on Stiefel manifolds. In the model, each agent evolves according to its own skew-symmetric natural frequency and interacts through a projected attraction toward a weighted average of neighboring states. When all natural frequencies coincide, the dynamics can be transformed into a gradient flow on a product manifold by passing to a suitable moving frame. In this study, we focus on the genuinely heterogeneous case in which the natural frequencies are not all identical and the gradient-flow structure is no longer available. For separable network topologies, we perform an orbital stability analysis and establish the emergence of asymptotic consensus under a suitable framework involving small initial diameter, small heterogeneity, and sufficiently large coupling strength. This improves upon the previous result in [Ha et al., Automatica 136 (2022)] by providing a sufficient regime whose size does not shrink with the number of agents. We also establish a uniform-in-time stability estimate with respect to the initial data under a homogeneous asymptotic complete-consensus assumption. In the small-diameter subregime with a fixed margin below 2 , the stability constants can be chosen explicitly.

The authors' abstract, as published at the source. Nonlinear Analysis, 2026 · DOI ↗