Standing and travelling waves in a spherical brain model: The Nunez model revisited
Physica D: Nonlinear Phenomena
Elsevier for North-Holland
Open Access funded by Wellcome Trust. Under a Creative Commons license: https://creativecommons.org/licenses/by/4.0/
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.
The authors would like to thank Stephan van Gils for his valuable input on the manuscript, and Paul Nunez for discussions about experimental and clinical issues. We are also grateful to the anonymous referees for their constructive comments. SV and SC were supported by the European Commission through the FP7 Marie Curie Initial Training Network 289146, NETT: Neural Engineering Transformative Technologies. Moreover, SV was generously supported by the Wellcome Trust Institutional Strategic Support Award (WT105618MA).
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.
Available online 8 March 2017