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
Breakspear, M., et al. «A Unifying Explanation of Primary Generalized Seizures Through Nonlinear Brain Modeling and Bifurcation Analysis». Cerebral Cortex, vol. 16, fasc. 9, 2005, pp. 1296–313, https://doi.org/10.1093/cercor/bhj072.
Cattell O., et al. «Understanding tonic-clonic seizure transitions as secondary bifurcations in a neural field model». Proceedings of the Royal Society A, In press, 2026.
Ermentrout, G. B., e J. D. Cowan. «Secondary Bifurcation in Neuronal Nets». SIAM Journal on Applied Mathematics, vol. 39, fasc. 2, 1980, pp. 323–40, https://doi.org/10.1137/0139028.
