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On the determination of the basin of attraction of discrete dynamical systems
Consider a discrete dynamical system given by the iteration x(n+1) = g(x(n)) with exponentially asymptotically stable fixed point (x) over bar. In this paper, we seek to study its basin of attraction A((x) over bar) using sublevel sets of Lyapunov functions. We prove the existence of a smooth Lyapunov function. Moreover, we present an approximation method of this Lyapunov function using radial basis functions. Error estimates show that one can determine every connected and bounded subset of the basin of attraction with this method. Examples include an application to the region of convergence of Newton's method.
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Publication status
- Published
Journal
Journal of Difference Equations and ApplicationsISSN
1023-6198Publisher
Taylor & FrancisExternal DOI
Issue
6Volume
13Page range
523-546Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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