S. Boccaletti, D.L. Valladares, L.M. Percora, H.P. Geffert and T. Carroll, “Reconstruction Embedding Spaces of Coupled Dynamical Systems from Multivariate Data”, Phys. Rev. E 65, 035204, (2002).
A method for reconstructing dimensions of subspaces for weakly coupled dynamical systems is offered. The
tool is able to extrapolate the subspace dimensions from the zero coupling limit, where the division of
dimensions as per the algorithm is exact. Implementation of the proposed technique to multivariate data
demonstrates its effectiveness in disentangling subspace dimensionalities also in the case of emergent synchronized
motions, for both numerical and experimental systems.