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 (Unpublished)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 nonautonomous systems, any relevant subset of the phase space, which now includes the time as one coordinate, is unbounded in tdirection. 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 firstorder 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 06:57 
Last Modified:  29 May 2015 18:40 
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