2405.03227
Symmetry and Dynamical Analysis of a Discrete Time Model: The Higher Order Berverton-Holt Equation
Mensah Folly-Gbetoula
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s canonical-coordinate derivation establishes S̃n = 1/zn and the linear recursion S̃n+k = An S̃n + Bn; iterating yields S̃kn+j = S̃j ∏ A + ∑ B ∏ A (their Eq. (2.18)–(2.20)). At that point, the paper erroneously writes zkn+j = 1/S̃kn+j = zj ∏ A + zj ∑ B ∏ A (Eq. (2.21)), and likewise in (2.22); the reciprocal is missing. The correct statement is 1/zkn+j equals that product–sum, i.e., zkn+j is its reciprocal. This is exactly what the model derives. Notably, the paper’s later specializations for periodic/constant coefficients (Eqs. (2.23)–(2.25)) coincide with the reciprocal form, indirectly confirming the earlier misprint (or error) in (2.21)–(2.22) .
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper applies symmetry methods to a nonautonomous higher-order Beverton–Holt equation and derives closed forms that facilitate periodicity and stability analyses. However, a central displayed formula for the general closed form (Eqs. (2.21)–(2.22)) drops a reciprocal, making the statement as written incorrect, even though subsequent specializations are consistent with the corrected expression. Because this error affects the main solution statement, I recommend major revisions to correct the formulas and audit related derivations.