Numerically simulated spatio-temporal dynamics of the heterogeneous neural field (left) and stationary states (right). Here the stationary state V0(x) is exponentially stable with the parameters of point (1) in Figure 2. The simulation starts close to the stationary state V(x,0) = V0(x) + ξ(x) with the random numbers ξ(x) taken from a zero-mean Gaussian distribution with variance 0.3. The plot on the left hand side shows the deviation from the stationary state V0(x). The plot on the right hand side shows the stationary states V0(x) (solid line) and the final field activity at large times V(x,t = 125) (dashed line) which is almost identical to V0(x). The spatial domain has length L = 1 with n = 300.