Understanding tonic–clonic seizure transitions as secondary bifurcations in a neural field model

Cattell, O. ; Mayora-Cebollero, A. (Universidad de Zaragoza) ; O'Dea, R. D. ; Barrio, R. (Universidad de Zaragoza) ; Coombes, S.

Resumen: 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 theorized 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. A linear stability analysis of the space-clamped model is used to uncover the conditions for a Hopf–Hopf bifurcation whereby two incommensurate frequencies can be excited. 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. We further show how spatio-temporal patterns of activity can evolve in the fully nonlinear regime using direct numerical simulations far from a Turing bifurcation.

Idioma: Inglés

DOI: 10.1098/rspa.2025.0452

Año: 2026

Publicado en: Proceedings - Royal Society. Mathematical, physical and engineering sciences 482, 2338 (2026), 20250452 [28 pp.]
ISSN: 1364-5021

Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2021-122961NB-I00
Financiación: info:eu-repo/grantAgreement/ES/DGA/E24-20R
Financiación: info:eu-repo/grantAgreement/ES/DGA/E24-23R
Financiación: info:eu-repo/grantAgreement/ES/DGA/LMP94_21
Financiación: info:eu-repo/grantAgreement/ES/MCINN/PID2024-156032NB-I00
Financiación: info:eu-repo/grantAgreement/EUR/MICINN/TED2021-130459B-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)