Metastable dynamics in heterogeneous neural fields.

Cordula Schwappach,Peter Beim Graben,Axel Hutt

doi:10.3389/fnsys.2015.00097

Abstract

We present numerical simulations of metastable states in heterogeneous neural fields that are connected along heteroclinic orbits. Such trajectories are possible representations of transient neural activity as observed, for example, in the electroencephalogram. Based on previous theoretical findings on learning algorithms for neural fields, we directly construct synaptic weight kernels from Lotka-Volterra neural population dynamics without supervised training approaches. We deliver a MATLAB neural field toolbox validated by two examples of one- and two-dimensional neural fields. We demonstrate trial-to-trial variability and distributed representations in our simulations which might therefore be regarded as a proof-of-concept for more advanced neural field models of metastable dynamics in neurophysiological data.

Highlights

Metastable states and transient dynamics between metastable states have received increasing interest in the neuroscientific community in recent time
While symmetric connectivity usually leads to Hopfield-type attractor neural networks (Hopfield, 1982; Hertz et al, 1991) where transient dynamics is only observed for the motion from a basin
One-dimensional Neural Field For the one-dimensional neural field we compare in Figure 2 the prescribed spatiotemporal dynamics as resulting from the order parameter expansion (Equation 7) with the solution of the Amari (Equation 8)

Summary

Introduction

Metastable states and transient dynamics between metastable states have received increasing interest in the neuroscientific community in recent time. For the analysis of human EEG, several segmentation techniques into metastable states have recently been suggested by Hutt (2004), Allefeld et al (2009), and beim Graben and Hutt (2015). Metastable EEG topographies or components of the eventrelated potential (ERP) have been identified with saddle-nodes in deterministic low-dimensional systems by Hutt et al (2000) and Hutt and Riedel (2003). The discoveries of winnerless competition (Rabinovich et al, 2001; Seliger et al, 2003) and heteroclinic orbits in neural population dynamics (Afraimovich et al, 2004a,b; Rabinovich et al, 2008b) led to better understanding of metastability and transient behavior in theoretical neuroscience. While symmetric connectivity usually leads to Hopfield-type attractor neural networks (Hopfield, 1982; Hertz et al, 1991) where transient dynamics is only observed for the motion from a basin

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Conclusion