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

Giesl, Peter and Wendland, Holger (2011) Numerical determination of the basin of attraction for exponentially asymptotically autonomous dynamical systems. Nonlinear Analysis: Theory, Methods and Applications, 74 (10). pp. 3191-3203. ISSN 0362-546X

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Abstract

Numerical methods to determine the basin of attraction for autonomous equations focus on a bounded subset of the phase space. For non-autonomous systems, any relevant subset of the phase space, which now includes the time as one coordinate, is unbounded in the t-direction. Hence, a numerical method would have to use infinitely many points. To overcome this problem, we introduce a transformation of the phase space. Restricting ourselves to exponentially asymptotically autonomous systems, we can map the infinite time interval to a finite, compact one. The basin of attraction of a solution becomes the basin of attraction of an exponentially stable equilibrium for an autonomous system. Now we are able to generalise numerical methods from the autonomous case. More precisely, we characterise a Lyapunov function 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
Depositing User: Peter Giesl
Date Deposited: 06 Feb 2012 19:12
Last Modified: 11 May 2012 14:37
URI: http://sro.sussex.ac.uk/id/eprint/19558
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