Correlation-driven instability in nonlinear networks.

<p>A) Threshold-quadratic input-rate transfer function. B,C) Raster plots of 6 second realizations of activity for weak and strong synaptic weights. Neurons 0–199 are excitatory and 200–240 are inhibitory. B) (<i>W</i>_<i>EE</i>, <i>W</i>_<i>EI</i>, <i>W</i>_<i>IE</i>, <i>W</i>_<i>II</i>) = (.025, −.1, .01, −.1) mV. C) (<i>W</i>_<i>EE</i>, <i>W</i>_<i>EI</i>, <i>W</i>_<i>IE</i>, <i>W</i>_<i>II</i>) = (1.5, −6, .6, −6) 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 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 accounting for impact of the next order (pairwise correlations’ influence on mean and triplet correlations’ influence on pairwise). Dots: simulation. All dots after the one-loop spectral radius crosses 1 represent results averaged over the time period before the activity diverges.