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Dynamics of non-expensive maps: Theory and Applications to discrete event systems


The objective of the research project is to investigate the dynamical behaviour of certain 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 designers of these systems are faced with a number of dynamical questions: What is the long-term behaviour of the system? What are its stability properties? How fast does it operate? To answer these questions one needs to analyse a model.

The main goal of the research project is to develop a theory for the dynamics of discrete event systems that can be modelled by so-called topical maps. Such a theory covers a variety of interesting systems and would be of practical value to engineers. In addition, it would advance the existing linear theory of max-plus systems to amore profound non-linear theory. The creation of such a theory is a mathematical challenge, as the standard dynamical systems techniques are not appropriate. To succeed, Dr Sparrow and I intend to develop novel techniques that are based on non-expansiveness properties of the system. We believe that, as a team, we could make considerable progress.

In addition to expanding my research experience, the fellowship would give me the opportunity to work in the dynamics group at Warwick University. It would allow me to collaborate and interact with some of the world's leaders in dynamics. By attending postgraduate courses, weekly seminars, workshops, and symposia I would become acquainted with a variety of pure and applied topics in dynamical systems and enrich my knowledge of this field. The extensive visitors programme of the Mathematics Institute would allow me to meet many scientists and become part of a large international network of researchers in dynamics.

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