# American Institute of Mathematical Sciences

October  2015, 20(8): 2453-2476. doi: 10.3934/dcdsb.2015.20.2453

## Grid refinement in the construction of Lyapunov functions using radial basis functions

 1 Department of Mathematics, University of Sussex, Falmer BN1 9QH, United Kingdom

Received  September 2014 Revised  January 2015 Published  August 2015

Lyapunov functions are a main tool to determine the domain of attraction of equilibria in dynamical systems. Recently, several methods have been presented to construct a Lyapunov function for a given system. In this paper, we improve the construction method for Lyapunov functions using Radial Basis Functions. We combine this method with a new grid refinement algorithm based on Voronoi diagrams. Starting with a coarse grid and applying the refinement algorithm, we thus manage to reduce the number of data points needed to construct Lyapunov functions. Finally, we give numerical examples to illustrate our algorithms.
Citation: Najla Mohammed, Peter Giesl. Grid refinement in the construction of Lyapunov functions using radial basis functions. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2453-2476. doi: 10.3934/dcdsb.2015.20.2453
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