| EPSRC Reference: |
GR/R94572/01 |
| Title: |
Global Manifolds in Slow-Fast Systems |
| Principal Investigator: |
Osinga, Professor HM |
| Other Investigators: |
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| Department: |
Engineering Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Fast Stream |
| Starts: |
01 October 2002 |
Ends: |
30 September 2005 |
Value (£): |
63,431
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Non-linear Systems Mathematics |
| Numerical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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This proposal is for a project studentship to develop and apply new algorithms for the computation of global invariant manifolds in slow-fast systems. Slow-fast systems appear as models in numerous applications, including mathematical biology, reaction kinetics, and engineering systems. The presence of different time scales leads to new phenomena, which makes classifying all possible dynamics and bifurcations in slow-fast systems a major challenge of dynamical systems theory. It is now generally recognised that progress will come by performing in-depth studies of specific examples, helped by advanced numerical techniques. This includes computing global stable and unstable manifolds of equilibria and periodic orbits, which requires the new methods developed in this project.As a testbed we will use a hierarchy of models related to the well-known Hodgkin-Huxley equations that model nerve axon dynamics. Later in the project, this work will be extended to other slow-fast systems, such as self-pulsating lasers and voltage collapse in models of power systems.
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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 |
| Summary |
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| Date Materialised |
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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.bris.ac.uk |