\[sec:HMF\] the heterogeneous mean-field approximation is used to reduce the set of equations. Section \[sec:RBN\] applies the formalism to random binary networks and consists of three subsections. In the first subsection the implicit equations for the steady states are derived and analyzed for saddle-node bifurcations. From this, the scaling of the critical coupling strength due to the network embedding is revealed. The second subsection addresses the limit of vanishing noise. Finally, the last subsection shows the results of the numerical solutions of the mean-field equations in presence of finite noise. Apart from the expected homogeneous ordered bistability that is known from globally coupled units [@Prager2003; @PrFaSchiZa07], inhomogeneous ordered and disordered states as well as tristable states are uncovered. These findings are confirmed via microscopic simulations using the original network structure. In these simulations the network exhibits a variable firing activity by approaching different steady states in dependence on the initial conditions. But the firing of the populations is not synchronized and thus the mean-field stays constant. The firing differs in the spike generating rates for the two populations and whether these are in the rest or excited states. The spike time statistics of individual units are discussed separately. Given that 