Dynamical ergodicity DDA reveals causal structure in time series

Determining synchronization, causality, and dynamical similarity in highly complex nonlinear systems like brains is challenging. Although distinct, these measures are related by the unknown deterministic structure of the underlying dynamical system. For two systems that are not independent on each o...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2021-10, Vol.31 (10), p.103108-103108
Main Authors: Lainscsek, Claudia, Cash, Sydney S., Sejnowski, Terrence J., Kurths, Jürgen
Format: Article
Language:English
Subjects:
Brain
Electroencephalography
Epilepsy
Ergodic processes
Humans
Nonlinear Dynamics
Nonlinear systems
Seizures
Similarity
Synchronism
Time series
Time synchronization
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Summary:Determining synchronization, causality, and dynamical similarity in highly complex nonlinear systems like brains is challenging. Although distinct, these measures are related by the unknown deterministic structure of the underlying dynamical system. For two systems that are not independent on each other, either because they result from a common process or they are already synchronized, causality measures typically fail. Here, we introduce dynamical ergodicity to assess dynamical similarity between time series and then combine this new measure with cross-dynamical delay differential analysis to estimate causal interactions between time series. We first tested this approach on simulated data from coupled Rössler systems where ground truth was known. We then applied it to intracranial electroencephalographic data from patients with epilepsy and found distinct dynamical states that were highly predictive of epileptic seizures.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0063724