The Exponential Ordering for Non-Autonomous Delay Systems with Applications to Compartmental Nicholson Systems

The paper proves, under the small-delay hypothesis r_i β_i^+ e^{d_i^+ r_i} < e together with (a1)–(a6) and uniform persistence at 0, the existence of a unique strongly positive almost periodic solution whose graph is a copy of the base and attracts all positive solutions with interior present value (Theorem 4.5 and its proof, including (4.9) and Corollary 4.6) . It also notes the trivial minimal set Ω×{0}, which persists without a persistence assumption , and establishes boundedness of solutions and the monotonicity/positivity properties under (4.8) (Theorem 4.2) . By contrast, the candidate’s Halanay-based fiber-contraction claim ignores the migration coupling in a way that does not yield a valid uniform contraction; more critically, a genuine global contraction on X would force the unique invariant graph to be the zero section, contradicting the sought strongly positive graph, unless one adds precisely the kind of persistence/positivity-away-from-zero hypothesis the paper assumes. Hence the model’s proof is flawed, while the paper’s argument is consistent and correct under its stated assumptions.