2017/10/31 by Leonardo L. Portes, Luis A. Aguirre, Luís A. Aguirre
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Chaos control and synchronization #Combinatorics #Complex Systems and Time Series Analysis #Mathematics #Mixed phase #Multivariate analysis #Multivariate statistics #Nonlinear Dynamics and Pattern Formation #Phase (matter) #Phase synchronization #Physics #Quantum mechanics #Singular spectrum analysis #Singular value decomposition #Statistics #Synchronization (alternating current) #Topology (electrical circuits) #nlin.CD
paper · pdf · doi:10.1007/s11071-019-04917-7
published as Nonlinear Dynamics, 96(3):2197--2209, 2019 · 22 pages, 9 figures
arxiv created 2017/10/31 · openalex publication_date 2019/04/01 · arxiv updated 2019/05/06 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/01
Multivariate singular spectrum analysis (M-SSA), with a varimax rotation of eigenvectors, was recently proposed to provide detailed information about phase synchronization in networks of nonlinear oscillators without any a priori need for phase estimation. The discriminatory power of M-SSA is often enhanced by using only the time series of the variable that provides the best observability of the node dynamics. In practice, however, diverse factors could prevent one to have access to this variable in some nodes and other variables should be used, resulting in a mixed set of variables. In the present work, the impact of this mixed measurement approach on the M-SSA is numerically investigated in networks of Rössler systems and cord oscillators. The results are threefold. First, a node measured by a poor variable, in terms of observability, becomes virtually invisible to the technique. Second, a side effect of using a poor variable is that the characterization of phase synchronization clustering of the \it other nodes is hindered by a small amount. This suggests that, given a network, synchronization analysis with M-SSA could be more reliable by not measuring those nodes that are accessible only through poor variables. Third, global phase synchronization could be detected even using only poor variables, given enough of them are measured. These insights could be useful in defining measurement strategies for both experimental design and real world applications for use with M-SSA.