Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5500212 | Physica D: Nonlinear Phenomena | 2017 | 51 Pages |
Abstract
The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or an integro-differential equation, have typically been studied in idealised one dimensional or planar settings. Here we revisit the original Nunez model to specifically address the role of spherical topology on spatio-temporal pattern generation. We do this using a mixture of Turing instability analysis, symmetric bifurcation theory, centre manifold reduction and direct simulations with a bespoke numerical scheme. In particular we examine standing and travelling wave solutions using normal form computation of primary and secondary bifurcations from a steady state. Interestingly, we observe spatio-temporal patterns which have counterparts seen in the EEG patterns of both epileptic and schizophrenic brain conditions.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
S. Visser, R. Nicks, O. Faugeras, S. Coombes,