Stability of Traveling Fronts in a Neural Field Model
We investigate the stability of traveling front solutions in the neural field model. This model has been studied intensively regarding propagating patterns with saturating Heaviside gain for neuron firing activity. Previous work has shown the existence of traveling fronts in the neural field model i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/2202 |
| _version_ | 1797602175131582464 |
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| author | Dominick Macaluso Yixin Guo |
| author_facet | Dominick Macaluso Yixin Guo |
| author_sort | Dominick Macaluso |
| collection | DOAJ |
| description | We investigate the stability of traveling front solutions in the neural field model. This model has been studied intensively regarding propagating patterns with saturating Heaviside gain for neuron firing activity. Previous work has shown the existence of traveling fronts in the neural field model in a more complex setting, using a nonsaturating piecewise linear gain. We aimed to study the stability of traveling fronts in the neural field model utilizing the Evans function. We attained the Evans function of traveling fronts using an integration of analytical derivations and a computational approach for the neural field model, with previously uninvestigated piecewise linear gain. Using this approach, we are able to identify both stable and unstable traveling fronts in the neural field model. |
| first_indexed | 2024-03-11T04:12:19Z |
| format | Article |
| id | doaj.art-8d84bfb21ccb480a84d957eddc4af058 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:12:19Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8d84bfb21ccb480a84d957eddc4af0582023-11-17T23:21:20ZengMDPI AGMathematics2227-73902023-05-01119220210.3390/math11092202Stability of Traveling Fronts in a Neural Field ModelDominick Macaluso0Yixin Guo1Department of Neurosurgery, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USADepartment of Mathematics, College of Arts and Sciences, Drexel University, Philadelphia, PA 19104, USAWe investigate the stability of traveling front solutions in the neural field model. This model has been studied intensively regarding propagating patterns with saturating Heaviside gain for neuron firing activity. Previous work has shown the existence of traveling fronts in the neural field model in a more complex setting, using a nonsaturating piecewise linear gain. We aimed to study the stability of traveling fronts in the neural field model utilizing the Evans function. We attained the Evans function of traveling fronts using an integration of analytical derivations and a computational approach for the neural field model, with previously uninvestigated piecewise linear gain. Using this approach, we are able to identify both stable and unstable traveling fronts in the neural field model.https://www.mdpi.com/2227-7390/11/9/2202neural field modelEvans functionordinary differential equationstraveling fronts |
| spellingShingle | Dominick Macaluso Yixin Guo Stability of Traveling Fronts in a Neural Field Model Mathematics neural field model Evans function ordinary differential equations traveling fronts |
| title | Stability of Traveling Fronts in a Neural Field Model |
| title_full | Stability of Traveling Fronts in a Neural Field Model |
| title_fullStr | Stability of Traveling Fronts in a Neural Field Model |
| title_full_unstemmed | Stability of Traveling Fronts in a Neural Field Model |
| title_short | Stability of Traveling Fronts in a Neural Field Model |
| title_sort | stability of traveling fronts in a neural field model |
| topic | neural field model Evans function ordinary differential equations traveling fronts |
| url | https://www.mdpi.com/2227-7390/11/9/2202 |
| work_keys_str_mv | AT dominickmacaluso stabilityoftravelingfrontsinaneuralfieldmodel AT yixinguo stabilityoftravelingfrontsinaneuralfieldmodel |