have been written in terms of the state vector ${\mathcal{P}_1}(t)=(P(1,t | k_1),P(1,t |  k_2))^\mathrm{T}$. With respect to the network these solutions are homogeneous states since both populations of the network are ordered in the same states.

![image](./2sNetBif_1k2_1k3.pdf){width="100.00000%"}

![image](./2sNetBif_1k2_1k8.pdf){width="100.00000%"}

![image](./2sNetBif_1k2_1k4.pdf){width="100.00000%"}

Figure \[fig:1k2\_1k8\] presents the qualitative behavior with a strong mismatch of the degrees of the two populations, namely $\alpha=4$. The graph shows that in this parameter region bistability of the two ordered states occurs for lower noise values. With vanishing $D$-values the states become $(0,0)$ and $(0,1)$. In difference to the previous case, the second solution $(0,1)$ is inhomogeneous with respect to the two populations in the network. In the $(0,1)$ state one population is ordered in state $0$ whereas the other approaches an ordered state with mean activity $1$. It is a result of the strong mismatch $\alpha$ of the degrees and of the asymmetry $\nu$ of the two populations. If, for example, the first smaller population with a higher degree is ordered in the excited state $1$, it is not able to excite the second larger population anymore. The latter remains in the ordered rest state $0$.

Also the coexistence of both scenarios is possible and give rise to 