Heteroclinic units acting as pacemakers: Entrained dynamics for cognitive processes

Bhumika Thakur, Hildegard Meyer-Ortmanns

incompletemedium confidence

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

Audit review

The paper establishes the model and documents entrainment phenomena primarily by simulation and qualitative bifurcation discussion (GLV units, 1L and 2L pacemakers; effects of δ, γP, γD, noise, and back-coupling) but does not supply a general, rigorous proof of sustained entrainment along chains or monotonicity laws; key claims are empirical (e.g., stronger forward coupling increases entrainment length; deeper CE for driven units decreases it; noise or small back-coupling prevent long stalls) . The candidate solution offers a plausible ISS/small‑gain framework and return‑map heuristics for heteroclinic slowdown, aligning with the paper’s qualitative observations, but it leaves proofs at a high level and makes a monotonicity claim in δb (for 2L) that conflicts with the paper’s chain-level findings that increasing back-coupling can reduce entrainment length via feedback from the right and eventual de-entrainment . Hence, both are incomplete: the paper for rigor, the model for gaps in assumptions and some overstatements.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The work compellingly documents entrainment by heteroclinic pacemakers using a coherent GLV framework across several topologies and parameter regimes. However, the central claims are empirical; the paper would benefit from precise definitions (entrainment length, time windows) and at least partial analytical guarantees or clearly delimited scope. The candidate model offers a promising analytical route (ISS/small-gain plus heteroclinic return-map heuristics), but to meet the standards of rigor, more assumptions and quantitative bounds are needed, and monotonicity statements involving back-coupling should be constrained to small-gain regimes.