Figure 4.

(A) Eigenvalues of the diffusion map operator on the oscillator density dynamic data, sorted in decreasing order and colored by the corresponding residual value produced by the local linear regression algorithm. The first eigenfunction ϕ₁ suffices to parameterize the behavior. (B) A plot demonstrating the correspondence between the discovered diffusion map coordinate ϕ₁ and the magnitude of the typical Kuramoto order parameter R. It clearly shows the one-to-one correspondence between the two, verifying that the diffusion map coordinate is an “equivalent” coarse variable to R for this system.