Providing a basin of attraction to a target region by computation of Lyapunov-like functions

In this paper, we present a method for computing a basin of attrac-tion to a target region for non-linear ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the co-efficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly. It iteratively refines these relaxations in order to ensure that, whenever a non-degenerate solu-tion exists, it will eventually be found by the algorithm. Applicatio