Network-Oriented Modeling and Analysis of Dynamics Based on Adaptive Temporal-Causal Networks

This paper discusses how Network-Oriented Modelling based on adaptive temporal-causal networks can be used to model and analyse dynamics and adaptivity of various processes. Adaptive temporal-causal network models incorporate a dynamic perspective on causal relations in which the states in the network change over time due to the causal relations, and these causal relations themselves also change over time. It is discussed how modelling and analysis of the dynamics of the behaviour of these network models can be performed. 1 Introduction Network-Oriented Modelling has been proposed as a modeling perspective suitable for processes that are highly dynamic, circular and interactive. In different application areas this modelling perspective has been proposed in different forms: in the context of modelling organisations and social systems, of modelling metabolic processes, and of modelling electromagnetic systems. To address dynamics well, Network-Oriented Modeling based on adaptive temporal-causal networks has been developed. This approach incorporates a continuous (real) time dimension. Adaptive temporal-causal network models are dynamic in two ways: their states change over time based on the caual relations in the network, but these causal relations may also change over time. As in such networks often many interrelating cycles occur, their emerging behaviour patterns are not always easy to predict or analyse. This may make it hard to evaluate whether observed outcomes of simulations are plausible or might be due to implementation errors. However, some specific types of properties can also be analysed by calculations in a mathematical manner, without performing simulations. Such properties that are 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 (and the mathematical analysis was done in a correct manner), then there will be some error in the implementation of the model. In this paper methods to analyse such properties of temporal-causal network models will be described. They will be illustrated for two types of adaptive temporal-causal network models: one based on Hebbian learning (Section 3), and one based on the homophily principle for dynamic connection weights in adaptive networks modelling social interaction (Section 4)