Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnections
We consider a neuronal network model with both axonal connections (in the form ofsynaptic coupling) and delayed non-local feedback connections. The kernel in thefeedback channel is assumed to be a standard non-local one, while forthe kernel in the synaptic coupling, four types are considered.The mai...
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AIMS Press
2010-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.421 |
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| author | Felicia Maria G. Magpantay Xingfu Zou |
| author_facet | Felicia Maria G. Magpantay Xingfu Zou |
| author_sort | Felicia Maria G. Magpantay |
| collection | DOAJ |
| description | We consider a neuronal network model with both axonal connections (in the form ofsynaptic coupling) and delayed non-local feedback connections. The kernel in thefeedback channel is assumed to be a standard non-local one, while forthe kernel in the synaptic coupling, four types are considered.The main concern is the existence of travelling wave front. By employingthe speed index function, we are able to obtain the existence of a travelling wavefront for each of these four types within certain range of model parameters.We are also able to describe how the feedback coupling strength andthe magnitude of the delay affect the wave speed. Some particular kernel functionsfor these four cases are chosen to numerically demonstrate thetheoretical results. |
| format | Article |
| id | doaj-art-ebe028ab1f974bad89a7a00339a0e839 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-ebe028ab1f974bad89a7a00339a0e8392025-01-24T02:00:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-03-017242144210.3934/mbe.2010.7.421Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnectionsFelicia Maria G. Magpantay0Xingfu Zou1Department of Mathematics and Statistics, McGill University, Montreal, QuebecDepartment of Mathematics and Statistics, McGill University, Montreal, QuebecWe consider a neuronal network model with both axonal connections (in the form ofsynaptic coupling) and delayed non-local feedback connections. The kernel in thefeedback channel is assumed to be a standard non-local one, while forthe kernel in the synaptic coupling, four types are considered.The main concern is the existence of travelling wave front. By employingthe speed index function, we are able to obtain the existence of a travelling wavefront for each of these four types within certain range of model parameters.We are also able to describe how the feedback coupling strength andthe magnitude of the delay affect the wave speed. Some particular kernel functionsfor these four cases are chosen to numerically demonstrate thetheoretical results.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.421speed index functionneuronal networksintegro-differential equationspatially non-localtravelling wavefront.delayfeedback |
| spellingShingle | Felicia Maria G. Magpantay Xingfu Zou Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnections Mathematical Biosciences and Engineering speed index function neuronal networks integro-differential equation spatially non-local travelling wavefront. delay feedback |
| title | Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnections |
| title_full | Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnections |
| title_fullStr | Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnections |
| title_full_unstemmed | Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnections |
| title_short | Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnections |
| title_sort | wave fronts in neuronal fields with nonlocalpost synaptic axonal connections and delayed nonlocal feedbackconnections |
| topic | speed index function neuronal networks integro-differential equation spatially non-local travelling wavefront. delay feedback |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.421 |
| work_keys_str_mv | AT feliciamariagmagpantay wavefrontsinneuronalfieldswithnonlocalpostsynapticaxonalconnectionsanddelayednonlocalfeedbackconnections AT xingfuzou wavefrontsinneuronalfieldswithnonlocalpostsynapticaxonalconnectionsanddelayednonlocalfeedbackconnections |