Delay differential equations with periodic coefficients: a numerical insight

The paper is explicitly a preliminary numerical study: it only demonstrates—in plots and parameter sweeps—that for certain forcing amplitudes and periods, solutions entrain to the forcing and adopt the same period, carefully stating this occurs “within the admissible range for the periods” and not as a universal theorem. It summarizes known autonomous results (e.g., a unique symmetric slowly oscillating period-4 solution for τ=1 under standard monotonic/odd hypotheses) and reports locking windows for particular b0(t), but provides no general proof of existence for all T or all small ε. The candidate solution attacks a stronger universal claim (“for every ε∈(0,ε0), for arbitrary T and T-periodic a1”) that the paper does not make; its two obstructions (minimum semi-cycle > τ and resonance failure when a1 is constant) are mathematically sound but aimed at a strawman. Hence, the paper’s scope is numerically correct but theoretically incomplete, and the model’s critique, while containing valid constraints, does not engage the actual claims in the paper and misses required hypotheses (e.g., hyperbolicity) for its continuation arguments. See the paper’s abstract and numerical sections emphasizing admissible ranges and locking intervals, rather than universal statements , and its setup and known autonomous results (including period-4 in the symmetric case) .