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Published April 15, 2023 | public
Journal Article

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


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.

Additional Information

© 2023 Elsevier. BH and HO acknowledge partial support by the Air Force Office of Scientific Research under MURI award number FA9550-20-1-0358 (Machine Learning and Physics-Based Modeling and Simulation). BH also acknowledges partial support from GUST as an External Research Fellow. The authors thank AmirHossein Jafarian for useful comments. Data availability: No data was used for the research described in the article. Code: The code of the numerical experiments in this paper can be found at https://github.com/Viviny/KMD-for-MEG-EEG-VdP. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional details

August 22, 2023
October 20, 2023