| EPSRC Reference: |
GR/L42742/01 |
| Title: |
DYNAMICS OF NON-EXPANDING MAPS: THEORY AND APPLICATION TO DISCRETE EVENT SYSTEMS |
| Principal Investigator: |
Sparrow, Professor C |
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| Department: |
Pure Maths and Mathematical Statistics |
| Organisation: |
University of Cambridge |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 July 1998 |
Ends: |
30 June 2001 |
Value (£): |
109,530
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Discrete event systems (including, for example, networks of linked processors) can be modelled by dynamical systems on R^n. In these applications, the coordinates of a vector x+R^n represent the times of events at each of n nodes, and it is very natural to consider mappings which are homogeneous, monotonic and non-expanding in the sup norm. The project aims, inter alia, to understand the dynamics of such mappings, including the important questions of conditions for the existence of cycle-time vectors and of the possible periodic behaviours. The set of systems defined by minmax functions is of particular interest; if we think of max only functions as being linear in a particular sense (in the max-plus algebra), minimax mappings are the natural setting in which to consider nonlinear problems, and these will be one central focus of research. More general questions about the dynamics of maps which are non-expanding in the sup norm are also relevant and of interest. Application (including those to related mathematical areas) are to discrete event systems, scheduling problems of various kinds, models of nonlinear diffusion and the theory of positive matrices.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.cam.ac.uk |