Dynamical Analysis of a Predator-Prey Model with Additif Allee Effect and Prey Group Defense

Core existence and local-stability results in the paper match the system’s algebra and Jacobian, and agree with the candidate’s derivations (model definition, nullclines, Jacobian, E0 and E1 stability in weak Allee, coexistence classification including E6 non-hyperbolicity and E4/E5 stability via det-sign arguments) . However, the paper repeatedly mislabels saddles as “saddle-node,” and claims a Hopf bifurcation “at the predator extinction equilibrium” in prose/abstract, while the analysis and figures actually indicate Hopf at a coexistence equilibrium (J22=0 at coexistence and det>0 there; triangular Jacobian on the P=0 axis precludes Hopf at E1) . The candidate’s solution is precise about the forward invasion at E1 (via a one-dimensional center-manifold normal form) and properly states Hopf as conditional at coexistence, without overclaiming. Thus, the paper’s core calculations are correct, but its bifurcation claims lack a rigorous proof and contain terminology/location inaccuracies; the model solution is correct and more careful conceptually.