2103.09613
SINGULARLY PERTURBED BOUNDARY-EQUILIBRIUM BIFURCATIONS
S. Jelbart, K. U. Kristiansen, M. Wechselberger
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The candidate solution reproduces the paper’s leading-order scalings and formulas for the saddle-node, Hopf, Bogdanov–Takens, and local homoclinic loci, using a direct asymptotic reduction. The paper derives the same results via blow-up and desingularized normal forms and proves supercriticality. A minor sign typo in the paper’s item (ii) is correctly flagged by the model; the paper itself consistently uses τ > 0 elsewhere for Hopf. Net: the results agree; methods differ.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The manuscript presents a comprehensive and rigorous analysis of singularly perturbed boundary-equilibrium bifurcations using blow-up methods, unifying all 12 BEB unfoldings and deriving precise asymptotics for local bifurcation curves and criticalities. The results are technically solid and broadly useful to the nonsmooth dynamics community. A minor sign typo related to the Hopf condition should be corrected; otherwise the presentation is clear and the logic is sound.