Fig. 7

Single-neuron marginal-probability density for the membrane potential (left) and the firing rate (right) in a network with topology \(K_{8}\) (top) and \(Q_{3}\) (bottom). The parameters used for the simulation are \(t=1\), \(\sigma=0.1\), and those of Table 1 and Eq. (7.1). The numerical probability density has been calculated by simulating equations in (2.1) \(1\mbox{,}000\mbox{,}000\) times with the Euler–Maruyama scheme and then by applying a Monte Carlo method, while the analytical density has been evaluated by integrating Eqs. (4.11) + (4.12) over all but one dimension. From the comparison it is easy to observe that the mean and the variance of the numerical simulations are in good agreement with the corresponding analytical quantities, even if the numerical probability density is not perfectly normal, due to relatively small higher-order corrections that have been neglected in our first-order perturbative approach