A note on microlocal kernel design for some slow–fast stochastic differential equations with critical transitions and application to EEG signals

Boumediene Hamzi, Houman Owhadi and Léo Paillet

Physica A: Statistical Mechanics and its Applications, 2023, vol. 616, issue C

Abstract: This technical note presents an extension of kernel model decomposition (KMD) for detecting critical transitions in some fast–slow random dynamical systems. The approach rests upon modifying KMD for reconstructing an observable by using a novel data-based time-frequency-phase kernel that allows to approximate signals with critical transitions. In particular, we apply the developed method for approximating the solution and detecting critical transitions in some prototypical slow–fast SDEs with critical transitions. We also apply it to detecting seizures in a multi-scale mesoscale nine-dimensional SDE model of brain activity.

Keywords: Kernel Mode Decomposition (KMD); Data-based kernels; Micro-local kernel design; Critical transitions; Slow–fast stochastic differential equations; Learning signal from data; Learning noise from data (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437123001383
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:616:y:2023:i:c:s0378437123001383

DOI: 10.1016/j.physa.2023.128583

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().