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.
Document type :
Conference papers
Complete list of metadatas

Cited literature [38 references]  Display  Hide  Download

https://hal-centralesupelec.archives-ouvertes.fr/hal-01813326
Contributor : Antoine Chaillet <>
Submitted on : Tuesday, June 12, 2018 - 11:28:59 AM
Last modification on : Thursday, October 25, 2018 - 12:02:22 PM
Long-term archiving on : Thursday, September 13, 2018 - 2:10:33 PM

File

170918 - Incremental stab neur...
Files produced by the author(s)

Identifiers

Citation

Georgios Detorakis, Antoine Chaillet. Incremental stability of spatiotemporal delayed dynamics and application to neural fields. 56th IEEE Conference on Decision and Control (CDC 2017), Dec 2017, Melbourne, Australia. ⟨10.1109/CDC.2017.8264558⟩. ⟨hal-01813326⟩

Share

Metrics

Record views

80

Files downloads

77