Attractor and saddle node dynamics in heterogeneous neural fields

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.