On the determination of the basin of attraction of discrete dynamical systems

Giesl, Peter (2007) On the determination of the basin of attraction of discrete dynamical systems. Journal of Difference Equations and Applications, 13 (6). pp. 523-546. ISSN 1023-6198

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Peter Giesl
Date Deposited: 06 Feb 2012 20:07
Last Modified: 10 Jul 2012 08:26
URI: http://sro.sussex.ac.uk/id/eprint/24183
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