Predator-prey ecosystem with group defence in prey against generalist predator

Sarit Maitra, Rajesh Ranjan Patra, Soumen Kundu

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 global asymptotic stability of the unique interior equilibrium for the predator–prey system via a convex (entropy-type) Lyapunov function, under two explicit inequalities (its (11)–(12)), and gives a complete algebraic reduction to a positive definite quadratic form. The candidate solution ultimately uses the same Lyapunov structure and recovers exactly the same two inequalities, hence reaches the same conclusion. The candidate additionally proposes a Bendixson–Dulac argument and a boundary/center-manifold analysis; these extra steps are not required for correctness and parts of them are only sketched. Overall, both are correct on the main result and essentially the same proof idea underlies the decisive step.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript provides a correct and well-motivated global stability result for a biologically relevant system using a standard but effective Lyapunov construction. The main theorem is sound and numerically illustrated. A few derivations in the proof are compressed and would benefit from expanded algebra to improve readability and rigor for a broad audience. The contribution is of solid specialist interest rather than field-leading novelty.