Linking structure and activity in nonlinear spiking networks
Fig 1
Dynamics approaching the firing-rate instability in threshold-quadratic networks.
A) Average firing rate of the excitatory neurons as synaptic weights are scaled. While the ordinate axis shows the excitatory-excitatory synaptic weight, all other weights are scaled with it. Solid lines: prediction of mean field theory. Dots: result of simulation. Inset: threshold-quadratic transfer function. B) Spectral radius of the stability matrix of mean field theory as synaptic weights are scaled. Stars indicate the weight values for the simulations below. C) Example realizations of activity for three different interaction strengths. As synapses become stronger, correlated activity becomes apparent. When synapses are strong enough the activity becomes unstable, even though the mean field theory is stable. All plotted firing rates in A) are averaged over the time period before the rates diverged (if they did). Left: (WEE, WEI, WIE, WII) = (.025, -.1, .01, -.1) mV. C). Middle: (WEE, WEI, WIE, WII) = (1, −4, .4, −4) mV. Right: (WEE, WEI, WIE, WII) = (1.5, −6, .6, −6) mV.