Correlation-driven instability in a non-Erdős-Rényi network with broadly distributed excitatory-excitatory weights.

A) Threshold-quadratic input-rate transfer function. B) Histogram of excitatory-excitatory synaptic weights with location parameter of 1.42 (mean of.29 mV), corresponding to the simulation in panel C. C) Raster plots of 6 second realizations of activity. Neurons 0–199 are excitatory and 200–240 are inhibitory. (W_EE, W_EI, W_IE, W_II) = (1.125, −4.5, .45, −4.5) mV. D-F) Average firing rate of the excitatory neurons (D), integral of the auto-covariance function of the summed population spike train (E), and spectral radius of the stability matrix of mean field theory (F) vs. excitatory-excitatory synaptic weight. While the mean excitatory-excitatory weight is plotted on the horizontal axis, all other synaptic weights increase proportionally with it. Black line: tree-level theory. Red line: one-loop correction. Dots: simulation. If a simulation exhibits divergent activity, the spike train statistics are averaged over the transient time before that divergence for visualization.