the rest state $s_i=0$. If being coupled, every population with given degree reaches a stationary probability to be in the excited state.

The precise number depends on the specific degree values, the noise intensity $D$ and the coupling constant $\sigma$. Generally for low coupling, respectively for high noise only a single solution exists, which is the disordered state of all populations. Lowering of noise, respectively increasing coupling, enlarges the number with multiple stable states, including inhomogeneous cases and the two homogeneous situations where all populations are in the rest or in the excited states. In general, it depends on the initial conditions which state will be populated.

Corresponding to the selected steady-state-solution the spiking rates differ. The spiking rate from rest to excited is determined by the stationary states of the population which the element belongs to. It is expressed by the rate given in where the specific solution has to be inserted. Such state dependent dynamical behavior of neuronal activity was recently discussed for phase oscillators in [@Kromer2014].

In this simplified model no Hopf-bifurcation can take place. All interactions have an aligning effect of the elements similar to a spin chain. Therefore, the existence of stable oscillating, chimaera state, 