Incremental stability of spatiotemporal delayed dynamics and application to neural fields

Abstract : We propose a Lyapounov-Krasovskii approach to study incremental stability in spatiotemporal dynamics with delays and their capability to be entrained by a periodic input. We then focus on delayed neural fields, which describe the spatiotemporal evolution of neuronal activity. We provide an explicit condition, involving the slope of the activation functions and the strength of coupling, under which delayed neural fields are incrementally stable regardless of communication delays. We finally show how this approach can be used to draw frequency profiles of neuronal populations.
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Pré-publication, Document de travail
This document is an extended version of the eponym paper published at the IEEE Conference on Deci.. 2017
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Soumis le : jeudi 14 septembre 2017 - 19:35:56
Dernière modification le : jeudi 5 avril 2018 - 12:30:05
Document(s) archivé(s) le : vendredi 15 décembre 2017 - 22:52:23

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  • HAL Id : hal-01587961, version 1

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Georgios Detorakis, Antoine Chaillet. Incremental stability of spatiotemporal delayed dynamics and application to neural fields. This document is an extended version of the eponym paper published at the IEEE Conference on Deci.. 2017. 〈hal-01587961〉

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