EPJ Nonlinear Biomed Phys
Volume 2, Number 1, December 2014
Advances in Neural Population Models and Their Networks
|Number of page(s)||17|
|Published online||09 May 2014|
Attractor and saddle node dynamics in heterogeneous neural fields
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
Accepted: 26 March 2014
Published online: 9 May 2014
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.
The work shows the linear stabiliy analysis of stationary states and the implementation of a nonlinear heteroclinic orbit.
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.
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.
Key words: Chaotic itinerancy / Linear stability / Heteroclinic orbits / Lotka-Volterra model
© The Author(s), 2014