Stability, convergence and bifurcation in some models of chemical kinetics

Abuthahir Abdulrahuman, Kalyan Chakrabarti, Gaurav Raina

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper derives the same characteristic equation, Hopf boundary ητ = arccos(−a/b)/√(b^2−a^2), and transversality Re(dλ/dη) > 0 using the same real/imaginary-part split as the model, and likewise gives the non‑oscillatory threshold bτe^{aτ} ≤ 1/e; see the paper’s equations (8)–(15) and (43)–(49) . The model mirrors these steps, adds a convexity check and a Lambert W cross‑check consistent with the paper’s result. Aside from a minor notation slip in the paper writing the stability inequality with ηc rather than η, the arguments align.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper provides correct and practically useful closed-form stability and convergence conditions for a retarded scalar DDE arising from a delayed-feedback chemical model. The Hopf boundary and transversality are derived cleanly, and the non-oscillatory threshold is sharp. A minor notation inconsistency (η vs ηc) should be corrected, and a brief note on the double-root interpretation at the 1/e boundary would further aid readers.