Impact of mixed measurements in detecting phase synchronization in networks using multivariate singular spectrum analysis

Multivariate singular spectrum analysis (M-SSA) is a useful tool to detect phase synchronization (PS) 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 dynamics. In the case of a network, however, diverse factors could prevent access to this variable at some nodes. Hence, other variables should be used instead, resulting in a mixed set of variables. The aim of the present work is to investigate, in a systematic way, the impact of using a mixed/incomplete measurement set in the M-SSA of chains of Rössler systems and cord oscillators. Results show that (i) the measurement of some variable from all oscillators does not guarantee detection of PS; (ii) typically one good observable per cluster should be recorded in order to detect PS among such clusters and that (iii) dropping poor variables does not reveal new PS transitions but improves on the resolution of what was already seen with such variables. The procedure is robust to noise.