Relaxation and self-sustained oscillations in the time elapsed neuron network model (Q2850690)
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scientific article; zbMATH DE number 6212915
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Relaxation and self-sustained oscillations in the time elapsed neuron network model |
scientific article; zbMATH DE number 6212915 |
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30 September 2013
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neuron networks
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desynchronization
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self-sustained oscillations
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Relaxation and self-sustained oscillations in the time elapsed neuron network model (English)
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The time elapsed model for neural networks has been introduced and studied by the authors in a previous paper [Nonlinearity 23, No. 1, 55--75 (2010; Zbl 1267.35239)]. The aim here is a further discussion on the convergence to asynchronous states and the construction of explicit periodic solutions in case assembly does not converge to the asynchronous state. After a presentation of the time elapsed model, results on convergence are proved in the sections `Dynamics of ensembles of disconnected neurons' and `Asynchronous activity for connected neuronal assemblies'. The section `Synchronous periodic oscillations in neuronal assemblies' is devoted to the construction of periodic solutions. Simulation results are shown.
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