Attractor and saddle node dynamics in heterogeneous neural fields

Abstract : We present analytical and numerical studies on the linear stability of spatially non-constant stationary states in heterogeneous neural elds for speci c synaptic interaction kernels. We nd that the stationary state obeys the Hammerstein equation and that the neural eld dynamics may obey a saddle-node bifurcation. Moreover our work takes up this nding and shows how to construct heteroclinic orbits built on a sequence of saddle nodes on multiple hierarchical levels on the basis of a Lotka-Volterra population dynamics.
Document type :
Journal articles
Complete list of metadatas

Cited literature [46 references]  Display  Hide  Download

https://hal.inria.fr/hal-00987789
Contributor : Axel Hutt <>
Submitted on : Tuesday, May 6, 2014 - 5:35:06 PM
Last modification on : Tuesday, December 18, 2018 - 4:40:21 PM
Long-term archiving on : Wednesday, August 6, 2014 - 1:45:35 PM

File

paper_text_figures.pdf
Files produced by the author(s)

Identifiers

Citation

Peter Beim Graben, Axel Hutt. Attractor and saddle node dynamics in heterogeneous neural fields. EPJ Nonlinear Biomedical Physics, 2014, 2, pp.4. ⟨10.1140/epjnbp17⟩. ⟨hal-00987789⟩

Share

Metrics

Record views

390

Files downloads

295