| EPSRC Reference: |
GR/J97243/01 |
| Title: |
NORMAL HYPERBOLICITY AND STABILTY IN CHAOTICALLY DRIVEN SYSTEMS |
| Principal Investigator: |
Davies, Professor M |
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| Department: |
Civil Environmental and Geomatic Eng |
| Organisation: |
UCL |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 1994 |
Ends: |
30 September 1997 |
Value (£): |
112,320
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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Summary on Grant Application Form |
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Although the idea of driving a dynamical system with a periodic signal is a common theme in much of nonlinear dynamics there has been little research into the effect of driving a system with a chaotic signal. Yet such systems are becoming of increasing interest in the application of dynamical systems theory to signal processing. A topical example of this is synchronisation between a dynamical system and a remote sub-system which has potential applications to secure communications. More generally, chaotically driven systems can be found in signal processing in the form of recursive filters driven by chaotic signals. These range from simple infinite impulse response (IIR) filters to nonlinear recursive least squares filters. However little is known about the stability and robustness of such systems. For example it has recently been observed that if an IIR filter is not sufficiently contracting then important invariants of the signal are modified. This phenomena may readily be interpreted as the destruction and/or loss of smoothness of a normally hyperbolic invariant manifold. Initially we propose to study the dynamics of some archetypal recursive filters to assess the effect that such a loss will have on their performance and stability. We also intend to analyse the special case of synchronisation and to determine its robustness to system imperfection. Ultimately we wish to develop a general framework for the analysis of such systems. This will require the extension of the theory of normally hyperbolic invariant manifolds in several directions. This is a problem that is closely related to the breakup of dimension reducing inertial manifolds in high dimensional systems.
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Potential use in non-academic contexts |
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| Description |
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Sectors submitted by the Researcher |
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