Issue |
EPJ Nonlinear Biomed Phys
Volume 2, Number 1, December 2014
Advances in Neural Population Models and Their Networks
|
|
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Article Number | 4 | |
Number of page(s) | 17 | |
DOI | https://doi.org/10.1140/epjnbp17 | |
Published online | 09 May 2014 |
https://doi.org/10.1140/epjnbp17
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
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.
Key words: Chaotic itinerancy / Linear stability / Heteroclinic orbits / Lotka-Volterra model
© The Author(s), 2014