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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.05073 |
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| _version_ | 1866916760684331008 |
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| author | Yeldesbay, Azamat Huguet, Gemma Daun, Silvia |
| author_facet | Yeldesbay, Azamat Huguet, Gemma Daun, Silvia |
| contents | We present a novel method of reconstructing the phase-amplitude dynamics directly from measured electrophysiological signals to estimate the coupling between brain regions. For this purpose, we use the recent advances in the field of phase-amplitude reduction of oscillatory systems, which allow the representation of an uncoupled oscillatory system as a phase-amplitude oscillator in a unique form using transformations (parameterizations) related to the eigenfunctions of the Koopman operator. By combining the parameterization method and the Fourier-Laplace averaging method for finding the eigenfunctions of the Koopman operator, we developed a method of assessing the transformation functions from the signals of the interacting oscillatory systems. The resulting reconstructed dynamical system is a network of phase-amplitude oscillators with the interactions between them represented as coupling functions in phase and amplitude coordinates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05073 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstruction of phase-amplitude dynamics from electrophysiological signals Yeldesbay, Azamat Huguet, Gemma Daun, Silvia Dynamical Systems We present a novel method of reconstructing the phase-amplitude dynamics directly from measured electrophysiological signals to estimate the coupling between brain regions. For this purpose, we use the recent advances in the field of phase-amplitude reduction of oscillatory systems, which allow the representation of an uncoupled oscillatory system as a phase-amplitude oscillator in a unique form using transformations (parameterizations) related to the eigenfunctions of the Koopman operator. By combining the parameterization method and the Fourier-Laplace averaging method for finding the eigenfunctions of the Koopman operator, we developed a method of assessing the transformation functions from the signals of the interacting oscillatory systems. The resulting reconstructed dynamical system is a network of phase-amplitude oscillators with the interactions between them represented as coupling functions in phase and amplitude coordinates. |
| title | Reconstruction of phase-amplitude dynamics from electrophysiological signals |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2406.05073 |