Neural field models with threshold noise

Thul, Ruediger; Coombes, Stephen; Laing, Carlo R.

Abstract

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.

Citation

Thul, R., Coombes, S., & Laing, C. R. (2016). Neural field models with threshold noise. Journal of Mathematical Neuroscience, 6, Article 3. https://doi.org/10.1186/s13408-016-0035-z

• Journal Article Type: Article
• Acceptance Date: Feb 19, 2016
• Publication Date: Mar 2, 2016
• Deposit Date: May 19, 2016
• Publicly Available Date: May 19, 2016
• Journal: Journal of Mathematical Neuroscience
• Electronic ISSN: 2190-8567
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 6
• Article Number: 3
• DOI: https://doi.org/10.1186/s13408-016-0035-z
• Keywords: Stochastic neural field, Interface dynamics, Fronts, Bumps, Non-Gaussian quenched disorder
• Public URL: https://nottingham-repository.worktribe.com/output/781880
• Publisher URL: http://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-016-0035-z