Modeling and Application of Self-organizing Systems Tutorial paper

This tutorial gives an overview about mathematical modeling methods for complex and self-organizing systems. Modeling can be used for the analysis and optimization of existing systems and for the design and engineering of new systems. In this tutorial we classify modeling methods into macro-level modeling and micro-level modeling. By using a micro-level model, the behaviors of all entities of the system and the interactions between these entities have to be specified. The state space of such a model is the Cartesian product of the state spaces of each entity. For a macro level, many micro-level states are aggregated into a single macro-level state. The macro level model describes only the behavior of the variables of interest. Another classification for modeling methods is the time space: The advance of time can either be modeled discrete or continuous. This tutorial contains short introductions to some modeling methods (e.g. Markov chains, cellular automata, recurrence equations, differential equations, . . . ) and a discussion about their possibilities for analysis, optimization, design and engineering of self-organizing systems. The applicability of the modeling methods are demonstrated in some use cases. Keywords-Self-Organization, Modeling, Systems