Fig. 5

Performance of the second and third equation, PRC versions (homogeneous inputs) with 5 ms delay. Simulations for three different amplitude combinations of \(\varDelta _{\mathrm{exc}}\) and \(\varDelta _{\mathrm{inh}}\). The figures on the left correspond to \(a_{\mathrm{exc}} = 1/30\), \(a_{\mathrm{inh}} = 2/30\), figures on the middle correspond to \(a_{\mathrm{exc}} = 2/30\), \(a_{\mathrm{inh}} = 2/30\), and the figures on the right correspond to \(a_{\mathrm{exc}} = 2/30\), \(a_{\mathrm{inh}} = 1/30\). The input rate for all simulations in a–d was \(r = 600\mbox{ Hz}\). Other than the input amplitudes, the only difference with the simulation of Fig. 4 is the delay value of 5 ms. a: Stationary phase PDFs for the oscillator with feedforward inhibition (red), with the second version of the equivalent PRC (green), and with the third version of the equivalent PRC (blue). b: PRCs used in the simulation. \(\varDelta _{\mathrm{exc}}\) (black), \(\varDelta _{\mathrm{inh}}\) (red), second version of \(\varDelta _{\mathrm{eq}}\) (green), third version of \(\varDelta _{\mathrm{eq}}\) (blue). c: Expected value of the inhibition as a function of the phase when the initial excitatory input arrives. The red curve comes from simulating the oscillator with feedforward inhibition, and the black curve comes from the approximation in Eq. (27). d: Cross-correlogram between the output spike trains of the oscillators with feedforward inhibition and with the third equivalent PRC. The horizontal axis indicates time shift, and the vertical axis the normalized spike count. Normalization was done by dividing the bin spike counts between the total number of spikes in the output of the oscillator with two PRCs. e: Firing rate response of the oscillators with feedforward inhibition (red), the second version of Equiv. PRC (green), and the third version of Equiv. PRC (blue) to five different levels of input rates. Input rates range from 240 Hz to 1200 Hz in constant increments of 240 Hz