Fig. 5

Different types of spiking behavior generated by the rate-reduced model (RNM). Top traces show the firing rate with \(r(t)=\kappa u(t)-a(t)-\theta\). Corresponding parameter values \((\theta,\kappa,\varepsilon,\gamma)\) are given in brackets. For small values of ε (i.e. a large time scale separation), there is excellent agreement with the corresponding examples of the full model (Fig. 2), which is quantified by comparing the integral of the spiking rate in the reduced model to the number of spikes in the full model. ( A ) Tonic spiking \((\frac{1}{10},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})\); \(27.18(23)\). ( B ) Spike-frequency adaptation \((\tfrac{1}{10},1,\tfrac{1}{1000},5)\); \(29.13(29)\). ( C ) Rebound spiking \((\tfrac{1}{50},2,\tfrac{1}{100},\tfrac{1}{5})\); \(7.84(8)\). ( D ) Accommodation \((\tfrac{3}{25},3,\tfrac{1}{50},\tfrac{2}{5})\); \(3.09 (3)\). ( E ) Spike latency \((\tfrac{1}{10},0,\tfrac{1}{200},\tfrac{2}{5})\); \(16.12(16)\). ( F ) Inhibition-induced spiking \((\tfrac{1}{50},-1,\tfrac{1}{500},\tfrac{2}{5})\); \(15.75(16)\)