Neural field models with threshold noise
The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling...
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| Format: | Article |
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Springer
2016
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| Online Access: | https://eprints.nottingham.ac.uk/33405/ |
| _version_ | 1848794624041156608 |
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| author | Thul, Ruediger Coombes, Stephen Laing, Carlo R. |
| author_facet | Thul, Ruediger Coombes, Stephen Laing, Carlo R. |
| author_sort | Thul, Ruediger |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches. |
| first_indexed | 2025-11-14T19:19:09Z |
| format | Article |
| id | nottingham-33405 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:19:09Z |
| publishDate | 2016 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-334052020-05-04T17:43:15Z https://eprints.nottingham.ac.uk/33405/ Neural field models with threshold noise Thul, Ruediger Coombes, Stephen Laing, Carlo R. The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches. Springer 2016-03-02 Article PeerReviewed Thul, Ruediger, Coombes, Stephen and Laing, Carlo R. (2016) Neural field models with threshold noise. Journal of Mathematical Neuroscience, 6 . 3/1-3/26. ISSN 2190-8567 Stochastic neural field Interface dynamics Fronts Bumps Non-Gaussian quenched disorder http://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-016-0035-z doi:10.1186/s13408-016-0035-z doi:10.1186/s13408-016-0035-z |
| spellingShingle | Stochastic neural field Interface dynamics Fronts Bumps Non-Gaussian quenched disorder Thul, Ruediger Coombes, Stephen Laing, Carlo R. Neural field models with threshold noise |
| title | Neural field models with threshold noise |
| title_full | Neural field models with threshold noise |
| title_fullStr | Neural field models with threshold noise |
| title_full_unstemmed | Neural field models with threshold noise |
| title_short | Neural field models with threshold noise |
| title_sort | neural field models with threshold noise |
| topic | Stochastic neural field Interface dynamics Fronts Bumps Non-Gaussian quenched disorder |
| url | https://eprints.nottingham.ac.uk/33405/ https://eprints.nottingham.ac.uk/33405/ https://eprints.nottingham.ac.uk/33405/ |