Construction of a global Lyapunov function using radial basis functions with a single operator (Q2641668)

The author studies the basin of attraction of an asymptotically stable equilibrium of a general autonomous ordinary differential equation. It is well-known that sublevel sets of Lyapunov functions provide subsets of the basin of attraction. The existence and smoothness of a Lyapunov function with certain, given orbital derivation is shown. By approximation of this Lyapunov function using radial basis functions, the author constructs a global Lyapunov function which determines each compact subsets of the basin of attraction. The results are applied on a chemostat model.