2501.02889
Bifurcations and stability of synchronized solutions in the Kuramoto model with uniformly spaced natural frequencies
Kazuyuki Yagasaki
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s statements (existence, branch structure, pitchfork/saddle-node locations, stability for discrete and continuum cases, and exponential counting) are supported by its theorems. The candidate solution independently rederives the same main conclusions using self-consistency, a turning-point criterion, and energy-form arguments. Minor deviations appear in the model’s continuum stability justification (it informally invokes a “rank-two linearization” and a fold argument), but the conclusions match the paper’s rigorous results.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper rigorously analyzes synchronized solutions in the Kuramoto model with uniformly spaced frequencies, unifying finite-n and continuum pictures. It proves clear results on existence, bifurcations, stability, and exponential counting. The exposition is solid; minor edits (e.g., a likely typographical 'O(2n)' vs 'O(2\^n)') and small clarifications would further improve readability. Overall, this is a valuable contribution to the synchronization/bifurcation literature.