We are analysing stochastic disturbances in networked systems with the aim of finding an appropriate and parsimonious statistical model for them. We have studied a simple statistical state model based on Ising model known from statistical physics. Our previous studies have derived an identification method for the model. We seek the ways to combine the statistical state model to real networked systems through mutual information between node states, the statistical significance of which is used as an absolute dependency measure of network nodes. In this paper we examine how the networked systems phenomena, such as coherence and hysteresis, appear in this statistical state model. In particular, our interest lies in the statistical dependence between the nodes when coherence and hysteresis occurs.