The Mathematical Institute, University of Oxford, Eprints Archive

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

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 (Unpublished)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)
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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