Strong coupling yields abrupt synchronization transitions in coupled oscillators

Jorge L. Ocampo-Espindola, István Z. Kiss, Christian Bick, Kyle C. A. Wedgwood

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 first‑order formulas for the bifurcation locations and cubic normal‑form coefficients and shows that at r=0 the in‑phase and anti‑phase pitchforks have opposite criticality on an open parameter set. The candidate solution follows the same normal‑form route and reaches the same conclusion. There is a minor sign inconsistency in the candidate’s intermediate approximations for the bifurcation locations and a small‑s expansion coefficient (−28 vs. the paper’s −26), but these do not affect the core claim that C̃(π) = −C̃(0) at r=0 and that the sign difference persists on an open set.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The work convincingly shows, via first-order normal-form analysis of a two-oscillator phase model with higher harmonics, that in-phase and anti-phase pitchfork bifurcations can have distinct criticality, and it supports the theory with computations and experiments. While the argument is asymptotic and uses heuristic continuity to pass from approximation to an open set in parameter space, the qualitative conclusion is well supported. Clarifying the smallness assumptions and transversality would further improve rigor and readability.