Time and frequency response characteristics of integrator (left panels) and differentiator (right panels). A. The temporal response of a leaky integrator to a constant-step stimulus (horizontal bar) consists of abrupt reflex increase/decrease of the response at stimulus onset/cessation followed by exponentially increasing/decaying (potentiation/afterdischarge) on/off transients. A leaky differentiator has similar reflex components but with exponentially decaying (accommodation) on-transients and rebound off-transients, which are opposite to those of an integrator (overlaying dotted lines). In both cases the off-transients may be rectified, with the response becoming monophasic (not shown) instead of biphasic. The time scales chosen are typical of oculomotor integrator and respiratory integrator. B. In the frequency domain, an integrator/differentiator behaves like a low-pass/high-pass filter. The pass-band in both cases is the frequency range where the neurotransmission gain (normalized to unity) is highest and relatively constant. The high and low cut-off frequencies (vertical dotted lines) of these filters are inversely proportional to the time constants of the corresponding integrator and differentiator shown in A. C. Examples of RC integrator (C = 3.77, R1 = 1.60, R2 = 24.0, R3 = 0.73) and differentiator (C = 1.0, R1 = 1.75, R2 = 24.0, R3 = 10.2) circuits with a current source (IS) input and voltage (V0) output. Units are arbitrary and RC values correspond to parameter values as defined in Eq. 1 (Appendix I) for integrator (a = 0.125; b = 0.125; c = 1; d = 0.5) and differentiator (a = 0.125; b = 0.125; c = -1; d = 1.5).