Global Dynamics of a Predator-Prey Model with State-Dependent Maturation-Delay

Qianqian Zhang, Yuan Yuan, Yunfei Lv, Shengqiang Liu

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves the permanence threshold R0 := n e^{-dj τ(0)} f(K,0)/d > 1 and extinction to (K,0,0) when R0 ≤ 1 for the state-dependent delay predator–prey system (2), using persistence theory (Hale–Waltman) and a Lyapunov-like functional V. The candidate solution establishes the same threshold via a different route: a sharp Halanay-type inequality for R0 < 1, a refined maximum-argument for the borderline R0 = 1, and standard persistence results for R0 > 1. The paper’s main conclusions match the model’s, though the equality case R0 = 1 in the paper’s Claim B uses an inequality sign that is not strictly justified as written; the candidate’s maximum-argument cleanly fills this gap. Overall, both are correct; the proofs differ.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript rigorously derives and analyzes a biologically grounded SDTD predator–prey model, establishing a sharp R0 threshold for permanence versus extinction and analyzing equilibrium stability. The arguments are largely correct and well-structured. A minor issue occurs at the borderline case R0=1 where a displayed inequality is asserted as strict; this is easily fixed using a standard refinement. Some expository points (positivity of x, details of the comparison/persistence steps) should be clarified to improve clarity.