Enhancing multivariate singular spectrum analysis for phase synchronization: The role of observability
Leonardo Luiz Portes, Luís A. Aguirre · Chaos An Interdisciplinary Journal of Nonlinear Science · 2016
Multivariate singular spectrum analysis (M-SSA) was recently adapted to study systems of coupled oscillators. It does not require an a priori definition for phase nor detailed knowledge of the individual oscillators, but it uses all the variables of each system. This aspect could be restrictive for practical applications, since usually just a few (sometimes only one) variables are measured. Based on dynamical systems and observability theories, we first show how to apply the M-SSA with only one variable and show the conditions to achieve good performance. Next, we provide numerical evidence that this single-variable approach enhances the explanatory power compared to the original M-SSA when computed with all the system variables. This could have important practical implications, as pointed out using benchmark oscillators.