is initiated, and (ii) that it is terminated slightly before the turning point of the $x_1$ nullcline. The latter effect becomes more pronounced if $a$ is increased or $\tau$ is decreased (Fig. \[fig:phaseportraits\]). Both lead to a shift of the initial starting point of the spike emission on the left branch of the nullcline towards $D$, and hence to a longer distance up to the middle branch of the nullcline which has to be overcome by the impulse $x_2$, hence to a larger turn-on delay $\delta$, and therefore to an earlier termination of the spike $x_1$. This explains that the firing phase is shortened, and the limit cycle loop is narrowed from both sides with increasing $a$ or decreasing $\tau$, see Fig. \[fig:phaseportraits\]. In the case of $a=1.05$ and $\tau=3$ (Fig. \[fig:phaseportraits\] (a)), the delay time is large enough for the two subsystems to nearly approach the fixed point $A$ before being perturbed again by the remote signal. If the delay time becomes much smaller, e.g., for $\tau=0.8$ (Fig. \[fig:phaseportraits\] (b)), the excitatory spike of the other subsystem arrives while the first system is still in the refractory phase, so that it cannot complete the return $D \to A$ to 