Modelling the Dynamics of Cross-Border Ideological Competition

Jose Segovia-Martin

incompletemedium confidence

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

Audit review

The paper formulates the 6D model and its 4D reduction, then reports a numerical “inflection point” near φ3≈0.0267 in the Figure 1 V–VI parameter set, but provides no stability or bifurcation analysis; it also incorrectly characterizes a parameter sensitivity as “deterministic chaos” and “sensitivity to initial conditions” . The candidate solution correctly identifies invariant faces and boundary equilibria of the reduced 4D system (paper Eq. (5)), shows they are φ3-independent in location, and explains the observed transition via two transcritical boundary collisions bracketing a stable interior branch; the reported values (≈0.026256 and ≈0.026708) reconcile the paper’s ‘≈0.0267’ observation .

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} note/short/other

\textbf{Justification:}

The manuscript offers a timely and interesting model but relies exclusively on simulation for its most consequential claims. The reported tipping near φ3≈0.0267 is plausible and well-motivated, yet no analytic equilibrium or stability analysis is provided. The text also mischaracterizes a parameter-induced transition as deterministic chaos and conflates parameter sensitivity with sensitivity to initial conditions. A revised version should correct terminology, add linear stability/bifurcation analysis of the reduced 4D system, and supply reproducible evidence for claims.