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

• Published in: Physica A 2023-04, Vol.616, p.128583, Article 128583
• Main Authors: Hamzi, Boumediene, Owhadi, Houman, Paillet, Léo
• Format: Article
• Language: English
• Subjects: Critical transitions; Data-based kernels; Kernel Mode Decomposition (KMD); Learning noise from data; Learning signal from data; Micro-local kernel design; Slow–fast stochastic differential equations
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2023.128583

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.