(a) shows the oscillation period vs. $\tau$ in a cut at $C=0.8$. Inset (b): schematic plot of the saddle-node bifurcation of a stable (red solid line) and unstable (blue dashed) limit cycle. The maximal oscillation amplitude is plotted vs. the delay time $\tau$ and the stable fixed point is plotted as a solid black line. The grey background marks the bistable region. Parameters: $a=1.05$, $\epsilon=0.01$. ](fig10.eps){width="50.00000%"}

![\[fig:isiplane\] Influence of delayed self-feedback upon coupled oscillations. The mean interspike interval (ISI) is color coded in the control parameter plane of the self-feedback gain $K$ and delay $\tau_K$. White areas mark regimes of irregular oscillations where the ISI variance becomes large ($>0.01$). Time series corresponding to points (a)-(f) are shown in Fig. \[fig:controlcases\]. Other parameters: $a=1.3$, $\epsilon=0.01$, $C=0.5$, $\tau=3$. ](fig11.eps){width=".5\textwidth"}

![\[fig:controlcases\] Different modes of oscillation corresponding to different self-feedback parameters $K$, $\tau$ (red solid lines: activators $x_i(t)$, green solid lines: inhibitors $y_i(t)$). (a), (b): Antiphase oscillations for (a) $K=0.05, \tau_K=3$ (period $T=6$) and (b) $K=0.5, \tau_K=2$ ($T=2$); (c), (d): In-phase oscillations for (c) $K=0.5, \tau_K=3$ (period $T=3$) and (d) $K=0.5, \tau_K=1.5$ ($T=1.5$); (e): Oscillator death for $K=0.9, \tau_K=0.9$; (f): Bursting pattern for $K=0.5, \tau_K=3.2$. Other parameters: $a=1.3$, $\epsilon=0.01$, $C=0.5, \tau=3$. ](fig12.eps){width=".9\textwidth"}

![\[fig:aps\] Average 