https://doi.org/10.1140/epjs/s11734-024-01332-x
Regular Article
Scaling features of correlated and anti-correlated data: numerical simulations and analysis of brain dynamics
1
Saratov State University, Astrakhanskaya Str. 83, 410012, Saratov, Russia
2
Regional Scientific and Educational Mathematical Center “Mathematics of Future Technologies”, 410012, Saratov, Russia
Received:
5
July
2024
Accepted:
5
September
2024
Published online:
23
September
2024
Recently, extended detrended fluctuation analysis (EDFA) has been proposed, which, along with the study of long-range power-law correlations, takes into account signal inhomogeneity, leading to a significant spread of local fluctuations for individual segments. This method introduces an additional scaling exponent to characterize the effects of nonstationarity. An unexpected result is negative values of the corresponding exponent for some processes. The paper examines the reason for this phenomenon and shows that the type of correlations plays a key role: the appearance of negative values is caused by the stationarity of the profiles of anti-correlated data. Understanding the relevant features allows us to achieve a more complete understanding of the effects of correlations type when applying the EDFA method, in particular, in diagnosing the complex dynamics of natural systems, including electrical activity of the brain.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
