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This article describes what we have termed the influence model, constructed to represent in a tractable way the dynamics of networked and interacting Markov chains. The constraints imposed on the influence model may restrict its modeling ability but permit explicit and detailed analysis and computation and still leave room for rather richly structured and novel behavior. We focus on the dynamic evolution of the system. The influence matrix H, in both the homogeneous and general cases, bears further study as an interesting generalization of familiar stochastic matrices. The influence model may also find use as a representation for stochastic signals of various kinds. The influence model is evidently related to other models of networked stochastic automata in the literature, but the details of the relationships remain to be worked out more explicitly in many cases. The generalizations embodied in the influence model could prove to be important degrees of freedom in particular applications.
Asavathiratham et al. (Sat,) studied this question.