Title: Mixed measurements and the detection of phase synchronization in networks,
Abstract: 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.