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

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Abstract

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.

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Acknowledgements

We thank Dr. Paul Castle for helpful discussions

Funding

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).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Western Australia, Nedlands, Perth, WA, 6009, Australia

    Leonardo L. Portes

  2. Programa de Pós-Graduação em Engenharia Elétrica, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, Belo Horizonte, MG, 31270-901, Brazil

    Leonardo L. Portes & Luis A. Aguirre

  3. Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, Belo Horizonte, MG, 31270-901, Brazil

    Luis A. Aguirre

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Portes, L.L., Aguirre, L.A. Impact of mixed measurements in detecting phase synchronization in networks using multivariate singular spectrum analysis. Nonlinear Dyn 96, 2197–2209 (2019). https://doi.org/10.1007/s11071-019-04917-7

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