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Journal Article

Dynamical ergodicity DDA reveals causal structure in time series


Lainscsek,  Claudia
External Organizations;

Cash,  Sydney S.
External Organizations;

Sejnowski,  Terrence J.
External Organizations;


Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Lainscsek, C., Cash, S. S., Sejnowski, T. J., Kurths, J. (2021): Dynamical ergodicity DDA reveals causal structure in time series. - Chaos, 31, 10, 103108.

Cite as: https://publications.pik-potsdam.de/pubman/item/item_26464
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.