The importance of different timings of excitatory and inhibitory pathways in neural field models
In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Ev...
| Main Authors: | , |
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| Format: | Article |
| Published: |
2005
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| Online Access: | https://eprints.nottingham.ac.uk/361/ |
| _version_ | 1848790399663996928 |
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| author | Laing, Carlo Coombes, Stephen |
| author_facet | Laing, Carlo Coombes, Stephen |
| author_sort | Laing, Carlo |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse $quot;anti-pulses,$quot; a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity. |
| first_indexed | 2025-11-14T18:12:00Z |
| format | Article |
| id | nottingham-361 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:12:00Z |
| publishDate | 2005 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-3612020-05-04T20:30:29Z https://eprints.nottingham.ac.uk/361/ The importance of different timings of excitatory and inhibitory pathways in neural field models Laing, Carlo Coombes, Stephen In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse $quot;anti-pulses,$quot; a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity. 2005-12 Article PeerReviewed Laing, Carlo and Coombes, Stephen (2005) The importance of different timings of excitatory and inhibitory pathways in neural field models. |
| spellingShingle | Laing, Carlo Coombes, Stephen The importance of different timings of excitatory and inhibitory pathways in neural field models |
| title | The importance of different timings of excitatory and inhibitory pathways in neural field models |
| title_full | The importance of different timings of excitatory and inhibitory pathways in neural field models |
| title_fullStr | The importance of different timings of excitatory and inhibitory pathways in neural field models |
| title_full_unstemmed | The importance of different timings of excitatory and inhibitory pathways in neural field models |
| title_short | The importance of different timings of excitatory and inhibitory pathways in neural field models |
| title_sort | importance of different timings of excitatory and inhibitory pathways in neural field models |
| url | https://eprints.nottingham.ac.uk/361/ |