Speaker
Description
Epilepsy is a dynamic complex disease involving a paroxysmal change in the activity of millions of neurons, often resulting in seizures. Tonic-clonic seizures are a particularly important class of these and have previously been theorised to arise in systems with an instability from one temporal rhythm to another via a quasi-periodic transition. We show that a recently introduced class of next generation neural field models has a sufficiently rich bifurcation structure to support such behaviour. This is used to seed a more exhaustive numerical bifurcation analysis that highlights the preponderance of the model to generate torus bifurcations. Since the neural field model is derived from a biophysically meaningful spiking tissue model we are able to highlight the neurobiological mechanisms that can underpin tonic-clonic seizures as they relate to levels of excitability, electrical and chemical synaptic coupling, and the speed of action potential propagation.
Bibliography
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title = {A {Unifying} {Explanation} of {Primary} {Generalized} {Seizures} {Through} {Nonlinear} {Brain} {Modeling} and {Bifurcation} {Analysis}},
volume = {16},
issn = {1460-2199, 1047-3211},
url = {http://academic.oup.com/cercor/article/16/9/1296/276340/A-Unifying-Explanation-of-Primary-Generalized},
doi = {10.1093/cercor/bhj072},
language = {en},
number = {9},
urldate = {2026-05-11},
journal = {Cerebral Cortex},
author = {Breakspear, M. and Roberts, J. A. and Terry, J. R. and Rodrigues, S. and Mahant, N. and Robinson, P. A.},
month = sep,
year = {2006},
pages = {1296--1313},
}
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author = {Cattell, O. and Mayora-Cebollero, A. and O'Dea, R. D. and Barrio, R. and Coombes, S.},
title = {Understanding tonic–clonic seizure transitions as secondary bifurcations in a neural field model},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
volume = {482},
number = {2338},
pages = {20250452},
year = {2026},
month = {05},
issn = {1364-5021},
doi = {10.1098/rspa.2025.0452},
url = {https://doi.org/10.1098/rspa.2025.0452},
eprint = {https://royalsocietypublishing.org/rspa/article-pdf/doi/10.1098/rspa.2025.0452/6140206/rspa.2025.0452.pdf},
}
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title = {Secondary {Bifurcation} in {Neuronal} {Nets}},
volume = {39},
issn = {0036-1399, 1095-712X},
url = {http://epubs.siam.org/doi/10.1137/0139028},
doi = {10.1137/0139028},
language = {en},
number = {2},
urldate = {2026-05-11},
journal = {SIAM Journal on Applied Mathematics},
author = {Ermentrout, G. B. and Cowan, J. D.},
month = oct,
year = {1980},
pages = {323--340},
}
