| EPSRC Reference: |
GR/R89721/01 |
| Title: |
Resonant Hopf Bifurcation and Applications |
| Principal Investigator: |
Stewart, Professor IN |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 2002 |
Ends: |
30 September 2002 |
Value (£): |
2,296
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Non-linear Systems Mathematics |
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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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The classical Hopf theorem states sufficient conditions for a periodic state to bifurcate from a steady state. A key hypothesis is the absence of resonances at the bifurcation point. However, such resonances are common in applications and are generic in systems with one free parameter. They can also be forced by symmetries. In recent years, much progress has been made in understanding the simpler cases of resonant Hopf bifurcation. The general area of this proposal is the more difficult cases, where more complicated dynamics arise, including 2-tori. The proposal covers three main topics. The most important is the nonsemisimple 1:1 resonance, which we approach through non-Hamiltonian perturbations of the Hamiltonian case. The chief question is: how much of the Hamiltonian dynamics persists, and in what form? In particular we focus on the possibility of monodromy in families of 2-tori. The second project is to find bifurcation scenarios leading to multirhythms - resonances forced by certain kinds of symmetry. The third project is to apply resonant Hopf bifurcation to vibrational modes of arrays of heat-exchanger tubes. Such vibrations are of interest in several areas of industry.
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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.warwick.ac.uk |