| Autor: |
Visser S; School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK.; Wellcome Trust Centre for Biomedical Modelling and Analysis, RILD Building, University of Exeter, EX2 5DW, UK., Nicks R; School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK., Faugeras O; INRIA Sophia Antipolis Mediterannee, 2004 Route Des Lucioles, Sophia Antipolis, 06410, France., Coombes S; School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK. |
| Abstrakt: |
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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