Ran the clean 3× comparison for N=32,33,64,65 at K=1.75. Odd-N always worse. The gap is larger than the variance between runs — this is a real effect. Still no explanation. Asked on the nonlinear-dynamics mailing list, no replies yet.
σ > 0.08 is where things get interesting. Above that threshold, the slip rate doesn't just increase — the slip distribution changes shape. Below σ=0.08, slips are Poisson-like. Above, they cluster. Something about the effective potential landscape flattening near the saddle?
Split the coupled-osc code into a proper library with a CLI wrapper. New features: HDF5 output, seed management, checkpoint/resume. Tagged v0.3.0. The v0.2.x API is broken, but nobody else was using it.
Thought about implementing power-law coupling (1/r^α) but decided to finish the ring topology analysis first. There are enough open questions with the nearest-neighbour case.
The review covers the homogeneous all-to-all case exhaustively but the section on sparse coupling is barely 3 pages long. They mention the ring topology parity effect in passing ("an interesting finite-size artifact") but don't pursue it. That's basically what I'm looking at.
Got the Euler-Maruyama integrator working. N=32 ring, fixed K, zero noise — phase-locking behaves exactly as expected from the Strogatz (2000) paper. Good sanity check. Next: add noise, increase N, start parameter sweeps.
Tried to derive K_c for ring topology with Gaussian frequency spread. Got stuck on the integral. The self-consistency equation for the order parameter turns into something that doesn't have an elementary closed form. Maybe numerical continuation is the way to go instead.
This started as a clock synchronization problem. If you have N nodes on a ring network trying to agree on time, the Kuramoto model is a decent first approximation. The noise term maps to oscillator jitter. K maps to the PLL loop bandwidth. σ maps to environmental drift. It's not a perfect analogy but it's good enough to be useful.
Putting together a minimal simulation framework in Python. Don't want to use existing packages — I need control over the integration and I want to understand every line. Will publish the repo once it's not embarrassing.
Last entry: 2026-07-14. No fixed update schedule.