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Abstract

The behavior and dynamics of complex systems are the focus of many research fields. The complexity of such systems comes not only from the number of their elements, but also from the unavoidable emergence of new properties of the system, which are not just a simple summation of the properties of its elements. The behavior of dynamic complex systems relates to a number of well developed models, the majority of which do not incorporate the modularity and the evolutionary dynamics of a system simultaneously. In this work, we deploy a Bayesian model that addresses this issue. Our model has been developed within the Random Finite Set Theory's framework. We introduced the stochastic evolution diagram as a novel mathematical tool to describe the evolutionary dynamics of complex modular systems. It has been shown how it could be used in real world applications. We have extended the idea of Bayesian network for non-stationary dynamic systems by defining a new concept "labeled-edge Bayesian network" and providing a Bayesian Dirichlet (BD) metric as its score function.