Fig. 6

Responses of the rate-reduced model (RNM) to periodic input. Top traces show the firing rate with \(r(t)= \kappa u(t)-a(t)-\theta\). ( A ) For \(\kappa=\frac{1}{10}\) the model acts as a low-pass filter. Input with an amplitude of \(\varphi=\frac{1}{5}\) yields a response in the firing rate for \(\omega=1\), whereas the firing rate remains zero for \(\omega=2\). In the former case, the integral of the spiking rate during one period is approximately 4.55, while there are 5 spikes per period in the full model (Fig. 4A). ( B ) For \(\kappa=2\), the reduced model acts as a high-pass filter. Input with amplitude \(\varphi=\tfrac{1}{10}\) elicits a firing rate response for \(\omega=2\), whereas a lower input frequency of \(\omega=1\) does not. In the former case, the integral of the spiking rate during one period is approximately 3.14, while there are 3 spikes per period in the full model (Fig. 4B). In both examples, \((\theta,\varepsilon,\gamma )= (\tfrac{1}{7},\tfrac{1}{200},2 )\)