Persistence and stability of generalized ribosome flow models with time-varying transition rates

Mihály A. Vághy, Gábor Szederkényi

incompletemedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s Theorem 4.5 claims a unique T-periodic attractor on every mass slice L_r under mere cooperativity and common period, with only a one-line proof via [29],[30]. As stated, this omits a necessary irreducibility/strong-connectivity (or strong monotonicity) hypothesis: in disconnected graphs, L_r generically contains a continuum of periodic solutions, so uniqueness fails. This gap is visible next to the paper’s own setup and examples . The candidate model solution correctly adds an irreducibility assumption and gets existence via periodic monotone-systems theory, but its uniqueness step appeals to a non-rigorous “strict ℓ1-contraction of the Poincaré map” for a nonlinear master-equation representation; that contraction is not justified under the given hypotheses and is known in the linear case only. Hence, both are incomplete: the paper for a missing hypothesis and the model for a missing justification of its key contraction step.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript offers a valuable synthesis linking generalized ribosome-flow models to CRN structure, with conservation laws and stability analyses. However, the central periodic entrainment result (Theorem 4.5) asserts uniqueness on each mass slice under cooperativity alone, supported only by a citation. This omits necessary structural hypotheses (irreducibility/strong monotonicity) and leads to an incorrect statement for disconnected graphs. The result should be restated with appropriate assumptions and a more detailed proof connecting the model’s structure to the conditions in the cited theorems.