2504.12821
Revisiting the Haken Lighthouse Model
S. Coombes
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper derives the synchronous period, constructs the timing-perturbation map, evaluates the kernel via Fourier/Dirac-comb (equivalently Poisson summation), and arrives at the same characteristic equation and slow-synapse/Hopf thresholds as the model. The model’s derivation mirrors the paper’s steps (invariant synchrony, period constraint, timing-map linearization, spectral projection, and Fourier–Laplace evaluation), differing only in presentation details. No substantive conflicts; assumptions align.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The manuscript presents a coherent and technically sound analysis of the Lighthouse model's synchronous dynamics across discrete and continuous settings. It leverages an event-based linearization framed in spike times and uses Fourier/Dirac-comb techniques to obtain a compact spectral condition, recovering static and delay-induced bifurcations and offering a continuum Turing analysis. The synthesis is valuable and accessible. Minor additions would further aid clarity, especially around the cancellation leading to the scalar characteristic equation and explicit assumptions on the synaptic kernel.