Construction of a local and global Lyapunov function for discrete dynamical systems using radial basis functions |
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Authors: | Peter Giesl |
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Institution: | Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9RF, UK |
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Abstract: | The basin of attraction of an asymptotically stable fixed point of the discrete dynamical system given by the iteration xn+1=g(xn) can be determined through sublevel sets of a Lyapunov function. In Giesl On the determination of the basin of attraction of discrete dynamical systems. J. Difference Equ. Appl. 13(6) (2007) 523–546] a Lyapunov function is constructed by approximating the solution of a difference equation using radial basis functions. However, the resulting Lyapunov function is non-local, i.e. it has no negative discrete orbital derivative in a neighborhood of the fixed point. In this paper we modify the construction method by using the Taylor polynomial and thus obtain a Lyapunov function with negative discrete orbital derivative both locally and globally. |
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Keywords: | MSC: 39A11 65Q05 37B25 37C25 |
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