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Fig. 4 | The Journal of Mathematical Neuroscience (JMN)

Fig. 4

From: Stochastic Synchronization in Purkinje Cells with Feedforward Inhibition Could Be Studied with Equivalent Phase-Response Curves

Fig. 4

Performance of the second and third equations, PRC versions (homogeneous inputs) with 1 ms delay. These figures compare the results of simulating an oscillator with feedforward inhibition against those of an oscillator with the equivalent PRC when the feedforward delay is 1 ms. The amplitudes for the excitatory and inhibitory PRCs are \(a_{\mathrm{exc}} = 2/30\), and \(a_{\mathrm{inh}} = 1/30\), respectively. The input rate is 600 Hz. 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: Phase resetting curves. Black = excitatory, red = inhibitory, green = second Equiv. PRC, blue = third Equiv. PRC. 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: Cross-correlogram between the output spike train of the oscillator with feedforward inhibition and a spike train with constant interspike intervals and the same frequency. Normalization was performed as in d. f: 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

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