Standing and travelling waves in a spherical brain model: the Nunez model revisited

Visser, Sid and Nicks, Rachel and Faugeras, Olivier and Coombes, Stephen (2017) Standing and travelling waves in a spherical brain model: the Nunez model revisited. Physica D: Nonlinear Phenomena, 349 . pp. 27-45. ISSN 0167-2789

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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, center 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.

Item Type: Article
Keywords: Neuronal networks, Integral equations, Space dependent delays, Dynamic pattern formation on a sphere, Normal form computation, Symmetric bifurcation theory
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1016/j.physd.2017.02.017
Depositing User: Coombes, Prof Stephen
Date Deposited: 10 Mar 2017 09:09
Last Modified: 18 Oct 2017 17:20
URI: http://eprints.nottingham.ac.uk/id/eprint/41182

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