Figure 2.

Anti-correlations in the degree distribution improve the stability of the low firing rate state (LFS). We compared the stability of finite-size networks with different degree correlation structure by iterating Equation 9 (which is Equation 1 without taking into account stochastic spiking). (A) The mean-field solution, corresponding to an infinite-size network, is simulated by assuming that the firing rate of each neuron is equal, yielding Equation 6, of which all roots are shown in the graph. (B) Mean firing rate r vs. coupling constant J in the mean-field limit for different values for the baseline firing rate r₀. When the LFS loses stability, the only remaining solution is the HFS. As a result the plotted firing rate suddenly jumps to the maximum possible rate of 100 Hz (corresponding to 1 spike per bin). (C) The range of stable coupling constants, which are between 0 and J_c, decreases with increasing baseline firing rate. (D) The firing rate r_c of the LFS just before it turns unstable increases linearly with r₀. (E) The stability of the LFS depends on system size and approaches the mean-field limit (cyan) gradually as network size N increases (baseline rate r₀ = 1 Hz). The anti-correlated network (blue) is always more stable than the ER (purple), correlated (red), and uncorrelated (green) networks. (F) The difference between the mean field J_c and that of the finite-size networks decreases with baseline firing rate (network size N = 2000).