Numerical determination of the basin of attraction for asymptotically autonomous dynamical systems

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

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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://sro.sussex.ac.uk/id/eprint/41690
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