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

In this paper, we present a method for computing a basin of attraction to a target region for polynomial 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 coefficients 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 nondegenerate solution exists, it will eventually be found by the algorithm. Application of an implementation to a range of benchmark problems shows the usefulness of the approach.