EFFECTS AND BIOLOGICAL CONSEQUENCES OF THE PREDATOR-MEDIATED APPARENT COMPETITION I: ODE MODELS

Yuan Lou, Weirun Tao, Zhi-An Wang

correctmedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves global stability by a unified entropy-type Lyapunov function E(t;Es) with carefully chosen weights Γi, yielding exact cancellation of cross terms and the conditions stated in Theorems 2.1–2.2 (including Λ1, Λ2, Λ∗) for Holling I and II, and GAS of Euv for θ ≥ L (see the definition of E(t;Es) in (5.3)–(5.4) and Lemmas 5.2–5.6) . The candidate solution independently constructs convex Lyapunov functions (including the primitives Fi for Holling II) and reaches the same GAS conclusions under the same parameter regimes (e.g., K1 ≤ λ1 + u∗, K2 ≤ λ2 + v∗ in Λ∗), with minor presentational gaps (e.g., a sketched boundedness argument) but no substantive contradictions.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The manuscript offers a rigorous and unified Lyapunov analysis for a biologically relevant predator–two-prey system, fully classifying the Holling I case and providing sharp sufficient conditions for Holling II. Proofs are correct and clean, the results are significant, and the numerical section is informative. Minor clarifications (e.g., explicit invariant-interval arguments in equality cases; an explicit note on the continuity convention for the entropy when a prey component is zero) would improve readability, but no major changes are needed.