Research

Attractor and saddle node dynamics in heterogeneous neural fields

⁷ Dept. of German Studies and Linguistics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany
⁸ Team Neurosys, INRIA Grand Est - Nancy, 615 rue du Jardin Botanique, 54602, Villers-les-Nancy, France
⁹ Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany

^* e-mail: Axel.Hutt@inria.fr

Received: 21 November 2013
Accepted: 26 March 2014
Published online: 9 May 2014

Abstract

Background

We present analytical and numerical studies on the linear stability of spatially non-constant stationary states in heterogeneous neural fields for specific synaptic interaction kernels.

Methods

The work shows the linear stabiliy analysis of stationary states and the implementation of a nonlinear heteroclinic orbit.

Results

We find that the stationary state obeys the Hammerstein equation and that the neural field dynamics may obey a saddle-node bifurcation. Moreover our work takes up this finding 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.

Conclusions

The work represents the basis for future implementation of meta-stable attractor dynamics observed experimentally in neural population activity, such as Local Field Potentials and EEG.