Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis

Grégory Faye 1 James Rankin 1, * Pascal Chossat 1, 2
* Corresponding author
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize work- ing (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equiva- lent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking- type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.
Liste complète des métadonnées

Cited literature [36 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00807366
Contributor : Pascal Chossat <>
Submitted on : Wednesday, April 3, 2013 - 2:21:00 PM
Last modification on : Thursday, May 3, 2018 - 1:32:58 PM
Document(s) archivé(s) le : Thursday, July 4, 2013 - 4:09:47 AM

File

faye-rankin-chossat.pdf
Publisher files allowed on an open archive

Identifiers

Citation

Grégory Faye, James Rankin, Pascal Chossat. Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis. Journal of Mathematical Biology, Springer Verlag (Germany), 2013, 66 (6), pp.1303-1338. ⟨10.1007/s00285-012-0532-y⟩. ⟨hal-00807366⟩

Share

Metrics

Record views

693

Files downloads

197