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Giesl, Peter and Wendland, Holger (2012) Numerical determination of the basin of attraction for asymptotically autonomous dynamical systems. Nonlinear Analysis: Theory, Methods and Applications, 75 (5). pp. 2823-2840. ISSN 0362-546X
Full text not available from this repository.Abstract
We develop a method to numerically analyse asymptotically autonomous systems of the form \dot{x} = f (t, x), where f (t, x) tends to g(x) as t → ∞. The rate of convergence is not limited to exponential, but may be polynomial, logarithmic or any other rate. For these systems, we propose a transformation of the infinite time interval to a finite, compact one, which reflects the rate of convergence of f to g. In the transformed system, the origin is an asymptotically stable equilibrium, which is exponentially stable in x-direction.Weconsider a Lyapunov function in this transformed system as a solution of a suitable linear first-order partial differential equation and approximate it using Radial Basis Functions.
| Item Type: | Article |
|---|---|
| Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Depositing User: | Peter Giesl |
| Date Deposited: | 30 Oct 2012 16:15 |
| Last Modified: | 30 Oct 2012 16:15 |
| URI: | http://srodev.sussex.ac.uk/id/eprint/41690 |