Fig. 2

The first two figures, (a) and (b), represent the evolution of the connectivity for original stochastic system (12), superimposed with averaged system (13), for two different values of ϵ: respectively $ϵ=0.01$ and $ϵ=0.001$, where we have chosen $ϵ={ϵ}_1={ϵ}_2$. Each color corresponds to the weight of an edge in a network made of $n=3$ neurons. As expected, it seems that the smaller ϵ, the better the approximation. This can be seen in the picture (c) where we have plotted the precision on the y-axis and ϵ on the x-axis. The parameters used here are $l=12$, $\mu =1$, $\kappa =100$, $\sigma =0.05$. The inputs have a random (but frozen) spatial structure and evolve according to a sinusoidal function.