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:#R##N##R##N##R##N#whether some values for the variables exist for which no change occurs (stationary points or equilibria), and how such values may depend on the values of the parameters of the model and/or the initial values for the variables#R##N##R##N##R##N#whether certain variables in the model converge to some limit value (equilibria) and how this may depend on the values of the parameters of the model and/or the initial values for the variables#R##N##R##N##R##N#whether or not certain variables will show monotonically increasing or decreasing values over time (monotonicity)#R##N##R##N##R##N#how fast a convergence to a limit value takes place (convergence speed)#R##N##R##N##R##N#whether situations occur in which no convergence takes place but in the end a specific sequence of values is repeated all the time (limit cycle)#R##N##R##N##R##N##R##N#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.
['Jan Treur']
Verification of temporal-causal network models by mathematical analysis