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

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

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.

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

• 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
• 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
• Public URL: https://nottingham-repository.worktribe.com/output/866258
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0167278916306352