the excited state possess an exponentially distributed waiting time, the spike trains are always nearly Poissonian. For a sharp-peaked waiting time density with no variance, the spike trains become highly coherent.

Two-state processes on complex networks {#sec:MF}
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Master equation of coupled two-state units {#sec:ME2}
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The stochastic two-state units considered in this work can switch between the states $0$ and $1$. They do so in a stochastic fashion, governed by the waiting time distributions $w_{0,i}(t)$ and $w_1(t)$ in the corresponding states, as explained Fig. \[fig:TSO\]. Focusing on excitable dynamics, state $0$ will be called the resting state and state $1$ the excited state.

![Sketch of the considered units and their topology. The two-state units with the waiting-time distributions $w_{0,i}(t)$ and $w_1(t)$ are embedded in a binary random network, as indicated by the dashed lines. In this example are five nodes with degree two and four nodes with degree four. The highlighted unit $i$ is one of the latter, hence its activation waiting-time distribution $w_{0,i}(t)$ is affected by the activity of four neighbors, as indicated by the dotted ellipse and the dotted arrow. []{data-label="fig:TSO"}](./newFig1){width=".49\textwidth"}

In this way, the transition from rest to excited, i.e. from state $0$ to state $1$, 