Travelling waves in models of neural tissue: from localised structures to periodic waves
We consider travelling waves (fronts, pulses and periodics) in spatially extended one dimensional neural field models. We demonstrate for an excitatory field with linear adaptation that, in addition to an expected stable pulse solution, a stable anti-pulse can exist. Varying the adaptation strength...
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| Format: | Article |
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Springer
2014
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| Online Access: | https://eprints.nottingham.ac.uk/41035/ |
| _version_ | 1848796181973434368 |
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| author | Meijer, Hil Coombes, Stephen |
| author_facet | Meijer, Hil Coombes, Stephen |
| author_sort | Meijer, Hil |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We consider travelling waves (fronts, pulses and periodics) in spatially extended one dimensional neural field models. We demonstrate for an excitatory field with linear adaptation that, in addition to an expected stable pulse solution, a stable anti-pulse can exist. Varying the adaptation strength we unravel the organizing centers of the bifurcation diagram for fronts and pulses, with a mixture of exact analysis for a Heaviside firing rate function and novel numerical schemes otherwise. These schemes, for non-local models with space-dependent delays, further allow for the construction and continuation of periodic waves. We use them to construct the dispersion curve – wave speed as a function of period – and find that they can be oscillatory and multi-valued, suggesting bistability of periodic waves. A kinematic theory predicts the onset of wave instabilities at stationary points in the dispersion curve, leading to period doubling behaviour, and is confirmed with direct numerical simulations. We end with a discussion of how the construction of dispersion curves may allow a useful classification scheme of neural field models for epileptic waves. |
| first_indexed | 2025-11-14T19:43:54Z |
| format | Article |
| id | nottingham-41035 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:54Z |
| publishDate | 2014 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410352020-05-04T16:45:21Z https://eprints.nottingham.ac.uk/41035/ Travelling waves in models of neural tissue: from localised structures to periodic waves Meijer, Hil Coombes, Stephen We consider travelling waves (fronts, pulses and periodics) in spatially extended one dimensional neural field models. We demonstrate for an excitatory field with linear adaptation that, in addition to an expected stable pulse solution, a stable anti-pulse can exist. Varying the adaptation strength we unravel the organizing centers of the bifurcation diagram for fronts and pulses, with a mixture of exact analysis for a Heaviside firing rate function and novel numerical schemes otherwise. These schemes, for non-local models with space-dependent delays, further allow for the construction and continuation of periodic waves. We use them to construct the dispersion curve – wave speed as a function of period – and find that they can be oscillatory and multi-valued, suggesting bistability of periodic waves. A kinematic theory predicts the onset of wave instabilities at stationary points in the dispersion curve, leading to period doubling behaviour, and is confirmed with direct numerical simulations. We end with a discussion of how the construction of dispersion curves may allow a useful classification scheme of neural field models for epileptic waves. Springer 2014-03-06 Article PeerReviewed Meijer, Hil and Coombes, Stephen (2014) Travelling waves in models of neural tissue: from localised structures to periodic waves. EPJ Nonlinear Biomedical Physics, 2 (3). pp. 1-18. ISSN 2195-0008 Neural field theory Brain wave equation Numerical continuation Anti-pulse Dispersion curve http://epjnonlinearbiomedphys.springeropen.com/articles/10.1140/epjnbp16 doi:10.1140/epjnbp16 doi:10.1140/epjnbp16 |
| spellingShingle | Neural field theory Brain wave equation Numerical continuation Anti-pulse Dispersion curve Meijer, Hil Coombes, Stephen Travelling waves in models of neural tissue: from localised structures to periodic waves |
| title | Travelling waves in models of neural tissue: from localised structures to periodic waves |
| title_full | Travelling waves in models of neural tissue: from localised structures to periodic waves |
| title_fullStr | Travelling waves in models of neural tissue: from localised structures to periodic waves |
| title_full_unstemmed | Travelling waves in models of neural tissue: from localised structures to periodic waves |
| title_short | Travelling waves in models of neural tissue: from localised structures to periodic waves |
| title_sort | travelling waves in models of neural tissue: from localised structures to periodic waves |
| topic | Neural field theory Brain wave equation Numerical continuation Anti-pulse Dispersion curve |
| url | https://eprints.nottingham.ac.uk/41035/ https://eprints.nottingham.ac.uk/41035/ https://eprints.nottingham.ac.uk/41035/ |