Fig. 2. Dynamical response of an intracellular adaptive variable a.

a Response to a stepwise signal: after a transient response, $a$ returns to its pre-stimulus state (within a small error $ϵ$). In the simplest case, the transient response is controlled by the activity shift timescale ${\tau }_a$ and the circuit feedback timescale ${\tau }_y$. Solid and dashed lines correspond to over-damped (${\tau }_a\ll {\tau }_y$) and under-damped (${\tau }_a\gg {\tau }_y$) situations, respectively. b Response to a sinusoidal signal at low (left) and high (right) frequencies. The phase shift ${\varphi }_a$ switches sign.