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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2507.23525 |
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| _version_ | 1866909713791188992 |
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| author | Cooray, Gerald Kaushallye |
| author_facet | Cooray, Gerald Kaushallye |
| contents | Cortical activity recorded through EEG and MEG reflects complex dynamics that span multiple temporal and spatial scales. Spectral analyses of these signals consistently reveal power-law behaviour, a hallmark of turbulent systems. In this paper, we derive a kinetic equation for neural field activity based on wave turbulence theory, highlighting how quantities such as energy and pseudo-particle density flow through wave-space (k-space) via direct and inverse cascades. We explore how different forms of nonlinearity, particularly 3-wave and 4-wave interactions, shape spectral features, including harmonic generation, spectral dispersion, and transient dynamics. While the observed power-law decays in empirical data are broadly consistent with turbulent cascades, variations across studies, such as the presence of dual decay rates or harmonic structures, point to a diversity of underlying mechanisms. We argue that although no single model fully explains all spectral observations, key constraints emerge: namely, that cortical dynamics exhibit features consistent with turbulent wave systems involving both single and dual cascades and a mixture of 3- and 4-wave interactions. This turbulence-based framework offers a principled and unifying approach to interpreting large-scale brain activity, including state transitions and seizure dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wave Turbulence and Cortical Dynamics Cooray, Gerald Kaushallye Adaptation and Self-Organizing Systems Cortical activity recorded through EEG and MEG reflects complex dynamics that span multiple temporal and spatial scales. Spectral analyses of these signals consistently reveal power-law behaviour, a hallmark of turbulent systems. In this paper, we derive a kinetic equation for neural field activity based on wave turbulence theory, highlighting how quantities such as energy and pseudo-particle density flow through wave-space (k-space) via direct and inverse cascades. We explore how different forms of nonlinearity, particularly 3-wave and 4-wave interactions, shape spectral features, including harmonic generation, spectral dispersion, and transient dynamics. While the observed power-law decays in empirical data are broadly consistent with turbulent cascades, variations across studies, such as the presence of dual decay rates or harmonic structures, point to a diversity of underlying mechanisms. We argue that although no single model fully explains all spectral observations, key constraints emerge: namely, that cortical dynamics exhibit features consistent with turbulent wave systems involving both single and dual cascades and a mixture of 3- and 4-wave interactions. This turbulence-based framework offers a principled and unifying approach to interpreting large-scale brain activity, including state transitions and seizure dynamics. |
| title | Wave Turbulence and Cortical Dynamics |
| topic | Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2507.23525 |