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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

Authors

Sid Visser s.visser@exeter.ac.uk

Rachel Nicks rachel.nicks@nottingham.ac.uk

Olivier Faugeras olivier.faugeras@inria.fr



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.

Journal Article Type Article
Publication Date Jun 15, 2017
Journal Physica D: Nonlinear Phenomena
Print ISSN 0167-2789
Electronic ISSN 0167-2789
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 349
APA6 Citation Visser, S., Nicks, R., Faugeras, O., & Coombes, S. (2017). Standing and travelling waves in a spherical brain model: the Nunez model revisited. Physica D: Nonlinear Phenomena, 349, https://doi.org/10.1016/j.physd.2017.02.017
DOI https://doi.org/10.1016/j.physd.2017.02.017
Keywords Neuronal networks, Integral equations, Space dependent delays, Dynamic pattern formation on a sphere, Normal form computation, Symmetric bifurcation theory
Publisher URL http://www.sciencedirect.com/science/article/pii/S0167278916306352
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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