| EPSRC Reference: |
GR/R23695/01 |
| Title: |
Local Bifurcations With Global Reinjection |
| Principal Investigator: |
Krauskopf, Professor B |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Engineering Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Fast Stream |
| Starts: |
01 November 2001 |
Ends: |
31 October 2004 |
Value (£): |
65,870
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| Communications |
No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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This grant is for a project studentship to work on a dynamical-systems analysis of a new class of global bifurcations: local codimension-two bifurcations in the presence of a global reinjection mechanism. The main example will be that of a saddle-node Hopf (SNH) bifurcation occurring at an equilibrium on a limit cycle. This mechanism has recently been found to be the organizing centre for the dynamics of the important semiconductor laser with optical injection. The bifurcation will be treated analytically via a new normal form, using both approximate Poincare mappings and the more rigorous Lin's method, in order to describe a complete unfolding. Specific numerical methods will be used for locating bifurcation curves and manifolds in example systems, especially the laser model. Stress will be given to global bifurcations in the unfolding, including large-excursion homoclinic and heteroclinic orbits, and also beyond-all-orders oscillations in curves of homoclinic orbits for the SNH without reinjection. Finally, the same style of analysis will be applied to obtain partial results for other bifurcations with reinjection, e.g. simultaneous saddle-node on a limit cycle and period-doubling.
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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 |