Giesl, Peter and Wendland, Holger (2010) *Numerical determination of the basin of attraction for exponentially asymptotically autonomous dynamical systems.* Technical Report. UNSPECIFIED. (Unpublished)

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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 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. 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: | Technical Report (Technical Report) |
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Subjects: | D - G > Dynamical systems and ergodic theory H - N > Numerical analysis |

Research Groups: | Numerical Analysis Group |

ID Code: | 978 |

Deposited By: | Lotti Ekert |

Deposited On: | 22 Oct 2010 07:57 |

Last Modified: | 22 Oct 2010 07:57 |

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