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Modelling the swarm: Analysing biological and engineered swarm systems

In this article, we discuss the current research efforts on swarm systems and on the motivation of mathematical modelling of such distributed and self-organizing systems. Obviously, a special emphasis is given to those articles which were carefully selected for the special issue at hand. These articles demonstrate how mathematical models of different kinds – bottom-up agent models and top-down model approaches – increase the understanding of natural swarm systems, for example, by investigating the efficiency in the self-regulation of social insect colonies. A second group of articles illustrates how mathematical models are used to generate and optimize artificial swarm systems as engineered in the field of swarm robotics. We discuss the common problems of such modelling efforts and highlight the importance of models as generators of hypotheses that suggest novel empiric experiments as well as the importance of empiric experimentation that results in meaningful model parameterizations. In summary, the special issue at hand, which is introduced by this article, gives a significant overview about the lines of research that are followed in the research of swarm systems today.