Delays in activity based neural networks
In this paper we study the effect of two distinct discrete delays on the dynamics of a Wilson-Cowan neural network. This activity based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discuss the interpretation of the delays in the langua...
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| Format: | Article |
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2008
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| Online Access: | https://eprints.nottingham.ac.uk/1000/ |
| _version_ | 1848790513391501312 |
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| author | Coombes, Stephen Laing, Carlo |
| author_facet | Coombes, Stephen Laing, Carlo |
| author_sort | Coombes, Stephen |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this paper we study the effect of two distinct discrete delays on the dynamics of a Wilson-Cowan neural network. This activity based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discuss the interpretation of the delays in the language of neurobiology and show how they can contribute to the generation of network rhythms. First we focus on the use of linear stability theory to show how to destabilise a fixed point, leading to the onset of oscillatory behaviour. Next we show for the choice of a Heaviside nonlinearity for the firing rate that such emergent oscillations can be either synchronous or anti-synchronous depending on whether inhibition or excitation dominates the network architecture. To probe the behaviour of smooth (sigmoidal) nonlinear firing rates we use a mixture of numerical bifurcation analysis and direct simulations, and uncover parameter windows that support chaotic behaviour. Finally we comment on the role of delays in the generation of bursting oscillations, and discuss natural extensions of the work in this paper. |
| first_indexed | 2025-11-14T18:13:48Z |
| format | Article |
| id | nottingham-1000 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:13:48Z |
| publishDate | 2008 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-10002020-05-04T20:27:37Z https://eprints.nottingham.ac.uk/1000/ Delays in activity based neural networks Coombes, Stephen Laing, Carlo In this paper we study the effect of two distinct discrete delays on the dynamics of a Wilson-Cowan neural network. This activity based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discuss the interpretation of the delays in the language of neurobiology and show how they can contribute to the generation of network rhythms. First we focus on the use of linear stability theory to show how to destabilise a fixed point, leading to the onset of oscillatory behaviour. Next we show for the choice of a Heaviside nonlinearity for the firing rate that such emergent oscillations can be either synchronous or anti-synchronous depending on whether inhibition or excitation dominates the network architecture. To probe the behaviour of smooth (sigmoidal) nonlinear firing rates we use a mixture of numerical bifurcation analysis and direct simulations, and uncover parameter windows that support chaotic behaviour. Finally we comment on the role of delays in the generation of bursting oscillations, and discuss natural extensions of the work in this paper. 2008 Article PeerReviewed Coombes, Stephen and Laing, Carlo (2008) Delays in activity based neural networks. Philosophical Transactions of the Royal Society A . ISSN 1364-503X (In Press) Wilson-Cowan networks multiple-delays phase-locking chaos http://publishing.royalsociety.org/index.cfm?page=1570 |
| spellingShingle | Wilson-Cowan networks multiple-delays phase-locking chaos Coombes, Stephen Laing, Carlo Delays in activity based neural networks |
| title | Delays in activity based neural networks |
| title_full | Delays in activity based neural networks |
| title_fullStr | Delays in activity based neural networks |
| title_full_unstemmed | Delays in activity based neural networks |
| title_short | Delays in activity based neural networks |
| title_sort | delays in activity based neural networks |
| topic | Wilson-Cowan networks multiple-delays phase-locking chaos |
| url | https://eprints.nottingham.ac.uk/1000/ https://eprints.nottingham.ac.uk/1000/ |