A note on a prey-predator model with constant-effort harvesting

The paper establishes that, for the scaled system dx/dt = x(1−x) − (x/(a+x^2))y − h1 x and dy/dt = δ y (1 − β y/x) − h2 y, the only ecologically meaningful equilibrium is E = (1−h1, 0), and the Jacobian at E is upper triangular with diagonal entries h1−1 and δ−h2; hence, if h1∈(0,1) and δ∈(0,h2), both eigenvalues are negative and E is a sink (Theorem 1). This is explicitly computed in the paper’s Section 3 and Theorem 1, including the Jacobian and eigenvalues . The candidate solution independently performs the same steps: verifies E is an equilibrium, computes the Jacobian entries, observes the upper-triangular form at E, and deduces both eigenvalues are negative under the same parameter restrictions. Both arrive at the same result via essentially the same linearization argument; no contradictions were found.