Verification of temporal-causal network models by mathematical analysis.

Usually dynamic properties of models can be analysed by conducting simulation experiments. But sometimes, as a kind of prediction properties can also be found by calculations in a mathematical manner, without performing simulations. Examples of properties that can be explored in such a manner are: Such properties found in an analytic mathematical manner can be used for verification of the model by checking them for the values observed in simulation experiments. If one of these properties is not fulfilled, then there will be some error in the implementation of the model. In this paper some methods to analyse such properties of dynamical models will be described and illustrated for the Hebbian learning model, and for dynamic connection strengths in social networks. The properties analysed by the methods discussed cover equilibria, increasing or decreasing trends, recurring patterns (limit cycles), and speed of convergence to equilibria. [ABSTRACT FROM AUTHOR]