Nonlinear Dynamics

, Volume 96, Issue 3, pp 2197–2209 | Cite as

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

  • Leonardo L. PortesEmail author
  • Luis A. Aguirre
Original Paper


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.


Phase synchronization Observability Time series analysis Chaos Multivariate singular spectrum analysis Networks Dynamical systems 



We thank Dr. Paul Castle for helpful discussions


This study was funded by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq–Brazil, Grant Numbers 302079/2011-4 and 502036/2014-1), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, grant number 3200 1010 015 P8) and Australian Research Council Discovery Grant (DP 180100718).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Western AustraliaNedlands, PerthAustralia
  2. 2.Programa de Pós-Graduação em Engenharia ElétricaUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  3. 3.Departamento de Engenharia EletrônicaUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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