Standing and travelling waves in a spherical brain model: the Nunez model revisited
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...
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| Format: | Article |
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Elsevier
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41182/ |
| _version_ | 1848796215389454336 |
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| author | Visser, Sid Nicks, Rachel Faugeras, Olivier Coombes, Stephen |
| author_facet | Visser, Sid Nicks, Rachel Faugeras, Olivier Coombes, Stephen |
| author_sort | Visser, Sid |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:44:26Z |
| format | Article |
| id | nottingham-41182 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:44:26Z |
| publishDate | 2017 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-411822020-05-04T18:50:20Z https://eprints.nottingham.ac.uk/41182/ Standing and travelling waves in a spherical brain model: the Nunez model revisited Visser, Sid Nicks, Rachel Faugeras, Olivier Coombes, Stephen 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. Elsevier 2017-06-15 Article PeerReviewed Visser, Sid, Nicks, Rachel, 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 Neuronal networks Integral equations Space dependent delays Dynamic pattern formation on a sphere Normal form computation Symmetric bifurcation theory http://www.sciencedirect.com/science/article/pii/S0167278916306352 doi:10.1016/j.physd.2017.02.017 doi:10.1016/j.physd.2017.02.017 |
| spellingShingle | Neuronal networks Integral equations Space dependent delays Dynamic pattern formation on a sphere Normal form computation Symmetric bifurcation theory Visser, Sid Nicks, Rachel Faugeras, Olivier Coombes, Stephen Standing and travelling waves in a spherical brain model: the Nunez model revisited |
| title | Standing and travelling waves in a spherical brain model: the Nunez model revisited |
| title_full | Standing and travelling waves in a spherical brain model: the Nunez model revisited |
| title_fullStr | Standing and travelling waves in a spherical brain model: the Nunez model revisited |
| title_full_unstemmed | Standing and travelling waves in a spherical brain model: the Nunez model revisited |
| title_short | Standing and travelling waves in a spherical brain model: the Nunez model revisited |
| title_sort | standing and travelling waves in a spherical brain model: the nunez model revisited |
| topic | Neuronal networks Integral equations Space dependent delays Dynamic pattern formation on a sphere Normal form computation Symmetric bifurcation theory |
| url | https://eprints.nottingham.ac.uk/41182/ https://eprints.nottingham.ac.uk/41182/ https://eprints.nottingham.ac.uk/41182/ |