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

Visser, Sid; Nicks, Rachel; Faugeras, Olivier; Coombes, Stephen

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


Sid Visser

Olivier Faugeras


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.

Journal Article Type Article
Acceptance Date Feb 28, 2017
Online Publication Date Mar 8, 2017
Publication Date Jun 15, 2017
Deposit Date Mar 10, 2017
Publicly Available Date Mar 10, 2017
Journal Physica D: Nonlinear Phenomena
Print ISSN 0167-2789
Electronic ISSN 0167-2789
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 349
Keywords Neuronal networks, Integral equations, Space dependent delays, Dynamic pattern formation on a sphere, Normal form computation, Symmetric bifurcation theory
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