Abstract
We study the basin of attraction of an asymptotically stable equilibrium of a general autonomous ordinary differential equation. Sublevel sets of Lyapunov functions provide subsets of the basin of attraction. In this paper we construct a Lyapunov function by approximation via radial basis functions. We show the existence and the smoothness of a Lyapunov function with certain, given orbital derivative. By approximation of this Lyapunov function via its orbital derivative using radial basis functions we obtain a global Lyapunov function and can thus determine each compact subset of the basin of attraction.
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