Final Activity Report Summary - EVENT DYNAMICS (Dynamics of Nonexpensive Maps: Theory and Applications to Discrete Event Systems) Discrete event systems are a useful abstraction to analyse the performance of certain man-made systems including: digital circuits, communication networks, and manufacturing systems. In practice the designers of these systems are faced with a number of questions concerning the stability and long-term behaviour of such systems. In this project we have analysed various models that generalise the usual max-plus models for such systems. For a variety of models we have shown that such systems settle in a stable periodic regime. In addition, we have obtained results concerning the geometric structure of the set of stable steady states. Our work will assist designers of discrete event systems to select the properties of the system such that it will display the desired behaviour. In addition, it will help engineers to analyse the behaviour of discrete event systems.From a theoretical point of view much insight has been gained. In particular, we have further developed a non-linear version of the classical Perron-Frobenius theory. Perron-Frobenius theory was developed by Perron and Frobenius at the beginning of twentieth century and encompasses positive linear dynamical systems. The non-linear version of this theory provides the underlying framework for the study of the behaviour of discrete event systems. During the project the Marie-Curie fellow started, in collaboration with Roger Nussbaum, to write a research monograph on non-linear Perron-Frobenius theory, which will be published by Cambridge University Press.
