Peter Giesl - Asymptotically autonomous systems
This webpage summarises the results of the project Calculating the Basin of Attraction in Asymptotically Autonomous Dynamical Systems
together with Holger Wendland (University of Oxford), May 2010-January 2011. The research was supported by the EPSRC Small Grants [EP/H051627/1, EP/I000860/1].
The results are published in
- P. Giesl and H. Wendland: Numerical determination of the basin of attraction for exponentially asymptotically autonomous dynamical systems. Nonlinear Anal. Nonlinear Anal. 74
No. 10 (2011), 3191-3203.
-
P. Giesl and H. Wendland: Numerical determination of the basin of attraction for asymptotically autonomous dynamical systems. Nonlinear Anal. 75
No. 5 (2012), 2823-2840.
This webpage contains the Matlab programs to calculate the basin of attraction of an
exponentially stable zero solution. The cases covered are
- Exponentially autonomous systems, where the right-hand side f(t,x) converges exponentially fast towards to g(x) as t goes to infinity, one-dimensional space variable x
- Polynomially autonomous systems, where the right-hand side f(t,x) converges polynomially fast towards to g(x) as t goes to infinity, one-dimensional space variable x
- Exponentially autonomous systems, where the right-hand side f(t,x) converges exponentially fast towards to g(x) as t goes to infinity, two-dimensional space variable x
Each part consists of an explanation and the Matlab files. The examples are taken from the above mentioned publications.
- Exponentially autonomous systems
-
Polynomially autonomous systems, 1D
- Polynomially autonomous systems, 2D
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Page last updated 30/12/11