| EPSRC Reference: |
GR/R87543/01 |
| Title: |
Chaotic dynamics and approximation by brownian motion in equivariant dynamical systems with continuous symmetry |
| Principal Investigator: |
Melbourne, Professor I |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Sch of Electronics & Physical Sciences |
| Organisation: |
University of Surrey |
| Scheme: |
Fast Stream |
| Starts: |
01 August 2002 |
Ends: |
31 July 2004 |
Value (£): |
20,106
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Panel History: |
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Summary on Grant Application Form |
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Equivariant dynamical systems is the theory of dynamical systems with symmetry, and its applicaiton to physical and experimental pattern forming systems and to numerical simulations of such systems. Initially, research emphasised local aspects of bifurcation theory in equivariant systems focusing on prechaotic features of pattern formation.Recently, interest has shifted to chaotic dynamics in systems with continuous symmetry and the implications for pattern forming systems. This includes statistical properties such as approximation by Browninan motion and topogical properties such as stable transitivity. The applicant, proposed visitors, and coworkers in Europe and the US have been at the forefront of this initiative.So far, this programme has been successful in explaining the hypermeander of sprial waves in excitable media, where the sprial tip appears to undergo a Brownian-like motion in the plane. This explanation incorporates techniques from local equivariant bifurcation theory, global dynamical systems, ergodic theory and probability theory. The aim of this proposal is to develop further the theoretical aspects of this work and to broaden the scope of its applicability. Intended applications, beyond the existing theory, include cellular flames, scroll waves and sprial waves on the surface of a sphere.
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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.surrey.ac.uk |