The Kuramoto model on a D-dimensional torus exhibits a first-order phase transition to synchronization arising from a saddle-node bifurcation, while the incoherent state stays stable.
O’Keeffe, A solvable two-dimensional swarmalator model
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Kuramoto model on the $D$-dimensional torus
The Kuramoto model on a D-dimensional torus exhibits a first-order phase transition to synchronization arising from a saddle-node bifurcation, while the incoherent state stays stable.