T_1\rangle /\langle T_2\rangle $ of the two subsystems, black solid curve: $\langle T_1\rangle$, red dashed curve: $\langle T_2\rangle $. Panels (a), (b), and (c) correspond to the case of moderate ($C=0.2$, $D_1=0.6$), weak ($C=0.1$, $D_1=0.6$), and strong ($C=0.2$, $D_1=0.15$) synchronization, respectively. Other parameters: $a=1.05$, $\epsilon_1=0.005$, $\epsilon_2=0.1$, $C=0.07$, $\tau=0$, $D_2=0.09$, $K=1.5$.](fig05c.eps "fig:"){width="0.32\linewidth"}

![\[fig:isi\_control\] Ratio of interspike intervals $\langle T_1\rangle / \langle
T_2\rangle$ in dependence on the feedback gain $K$ and the time delay $\tau$ for (a) moderate ($C=0.2$, $D_1=0.6$), (b) weak ($C=0.1$, $D_1=0.6$), and (c) strong ($C=0.2$, $D_1=0.15$) synchronization. Other parameters as in Fig. \[fig2\](c).](fig06.eps){width="\linewidth"}

Since we are interested in the effects of a control force on the synchronization, in the following we consider three different cases: moderately, weakly, and strongly synchronized systems given by the specific choices of the coupling strength and noise intensity in the first subsystem. These different cases of stochastic synchronization are marked as black dots in Fig. \[fig2\]. As a measure to quantify changes in the synchronization due to the control force, we consider the ratio of average interspike intervals. In the presence of a control force, i.e., $K\neq 0$, the cooperativity can be influenced by varying the feedback gain $K$ and the time delay $\tau_K$.

