Abstract : We present analytical and numerical studies on the linear stability of spatially non-constant stationary states in heterogeneous neural elds for speci c synaptic interaction kernels. We nd that the stationary state obeys the Hammerstein equation and that the neural eld dynamics may obey a saddle-node bifurcation. Moreover our work takes up this nding 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.
