Category: Nonlinear Dyn.

Summary: Locating the coupling strength where a large two-dimensional Kuramoto lattice switches from incoherent motion to macroscopic phase synchronization.

Coupled oscillators often show a collective synchronization transition, but the sharpness and location of that transition depend strongly on geometry and local coupling. This experiment studies a large nearest-neighbor Kuramoto lattice in two dimensions and asks for the critical coupling where the global order parameter rises from near zero to near one.

Instead of scanning all coupling values uniformly, the simulation treats candidate couplings like branches in an adaptive search. Clearly synchronized or clearly desynchronized values are pruned, while uncertain couplings receive deeper time evolution and more compute until the transition window is narrowed.

That strategy is useful because long transients near criticality are expensive, especially on large grids. The result is a direct estimate of the synchronization threshold that concentrates computation on the part of parameter space where the answer actually changes.

Method: Adaptive time-stepping search on a 256 x 256 nearest-neighbor Kuramoto lattice, pruning settled couplings and deepening probes near the transition.

What is measured: Critical coupling bracket, global order parameter, probe depth, and synchronized versus desynchronized classifications.