2008.11019
Global Stability and Periodicity in a Glucose-Insulin Regulation Model with a Single Delay
M. Angelova, G. Beliakov, A. Ivanov, S. Shelyag
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s main statements match the candidate solution, but the paper provides only sketches for the periodic-orbit parts (Theorems 3.2–3.4) and leans on numerics and outlines rather than complete proofs, while the model’s solution supplies a sounder route via large-delay singular perturbation but also asserts unproven equalities for liminf/limsup and uses a heuristic linearization for local stability. Thus both are broadly correct in thrust but each leaves gaps.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript’s organizing principle—reducing the RFDE’s long-time dynamics to a limiting interval map—is elegant and compelling. The delay-independent global stability result is clean. The periodicity, multiplicity, and coexistence claims are well motivated and supported numerically, but the existence proofs are outlined rather than completed. With detailed arguments (or precise citations) for the fixed-point index route and clearer spectral conditions, the work would be a solid contribution.