on the $N$ nodes of a complex network. Each stochastic element receives the output from the units to which it is linked in the network by edges. This coupling is mathematically realized by introduction of the adjacency matrix $\tens{A}$. The activation rate $\gamma_i$ from state $0$ to state $1$ of the $i$th node $i\in\{1,\dots,N\}$ is assumed to depend on a signal function $f_i(t)$ $$\begin{aligned}
    \gamma_i &= \gamma[f_i(t)],\end{aligned}$$ which contains the adjacency matrix $$\begin{aligned}
    f_i(t) &= \frac{1}{N}\,\sum_{j=1}^N A_{ij}\, s_j(t).
    \label{eq:output1}\end{aligned}$$ Therein, $s_j(t)$ is the output signal of node $j$ depending on its state. In this work, undirected and unweighted networks are considered, hence the adjacency matrix is symmetric with elements $A_{ij}=1$, if the units $i$ and $j$ are connected, otherwise $A_{ij}=0$.

Typically, excitable systems stay in the resting state where no output is produced. Upon sufficient excitation they drastically change their intrinsic dynamics which is emitted as a signal. Here such “spiking” is modeled by a two-valued output function $s_j(t)$, which can take the values $1$ in the excited state and $0$ otherwise. This setting is motivated by neuronal activity or excitable lasers. A symmetric choice would be more appropriate in order to model magnetic spins.

Eventually, in accordance with previous 