2508.07942
Discrete Dynamics of a Phytoplankton-Zooplankton Model with Toxin-Mediated Interactions
Sobirjon Shoyimardonov
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
Both the paper and the candidate solution correctly establish a Neimark–Sacker bifurcation at E1 and the supercritical/subcritical test via the sign of the first Lyapunov coefficient. However, the paper’s Theorem 3 omits the standard nondegeneracy hypothesis L ≠ 0 in its formal statement, while the model explicitly assumes it. The model’s derivation also captures the discrete normal-form reduction and radial dynamics; its use of ∂β q at the fixed point yields the correct transversality sign though not the exact coefficient used in the paper’s anchored Jacobian calculation.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript gives a careful, largely standard Neimark–Sacker analysis for a discrete ecological model, including explicit expansions and numerical corroboration. The argument is correct in substance; the sole notable omission is the explicit nondegeneracy hypothesis L ≠ 0 in Theorem 3. Adding this and a citation to a standard normal-form reference would address completeness and help readers.