| EPSRC Reference: |
EP/H051627/1 |
| Title: |
Calculating the Basin of Attraction in Asymptotically Autonomous Dynamical Systems |
| Principal Investigator: |
Giesl, Professor P |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Sch of Mathematical & Physical Sciences |
| Organisation: |
University of Sussex |
| Scheme: |
Standard Research |
| Starts: |
01 May 2010 |
Ends: |
31 March 2011 |
Value (£): |
6,568
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| EPSRC Research Topic Classifications: |
| 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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Ordinary differential equations (ODEs) are a major modelling tool in all sciences, for example mechanical systems in physics, population dynamics in biology, reactions in chemistry, price developments in economics and many more. Both for deriving the model and for its analysis it is crucial to understand the dynamical properties of an ODE. Nonautonomous ODEs are equations where the right-hand side explicitly depends on the time t, e.g. through a time-dependent force. They include asymptotically autonomous systems, where the right-hand side tends to an autonomous, i.e. time-independent, function as time tends to infinity. Dynamical systems are interested in the long-time behaviour of solutions. Although the equation converges to an autonomous one as time tends to infinity, not all properties of the limiting autonomous equation carry over to the nonautonomous one. In particular, the basin of attraction of a solution consisting of all points approaching this solution, is a nonautonomous object and can only be determined by considering the nonautonomous equation.However, not only the analytical, but also the numerical analysis of nonautonomous ODEs faces the difficulty that any interesting set is unbounded in the time direction. This makes a direct application of numerical tools from autonomous dynamical systems difficult, since one would need infinitely many grid points for the approximation. The main purpose of this project is to develop new tools, both in dynamical systems and in numerical analysis, to overcome this problem and to derive numerical methods for the analysis of nonautonomous systems. Within dynamical systems, the infinite time interval of the nonautonomous system will be transformed into a finite one; in numerical analysis a method will be developed to distinguish between the different dependencies with respect to the time and the space variables. The new method will be studied theoretically, including error estimates, and, moreover, be implemented into a computer program.
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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: |
http://www.maths.sussex.ac.uk/~giesl/asymptaut.html |
| Further Information: |
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| Organisation Website: |
http://www.sussex.ac.uk |