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

journal contribution
posted on 2023-06-07, 22:12 authored by Peter GieslPeter Giesl, Holger Wendland
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.

History

Publication status

  • Published

Journal

Nonlinear Analysis: Theory, Methods and Applications

ISSN

0362-546X

Publisher

Elsevier

Issue

10

Volume

74

Page range

3191-3203

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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