Graphical Representation of Separatrices of Attraction Basins in Two and Three Dimensional Dynamical Systems

In this paper we consider the problem of reconstructing separatrices in dynamical systems. In particular, here we aim at partitioning the domain approximating the boundaries of the basins of attraction of different stable equilibria. We start from the 2D case sketched in [Cavoretto et al. (2011)] and the approximation scheme presented in [Cavoretto et al. (2011); Cavoretto et al. (2015)], and then we extend the reconstruction scheme of separatrices in the cases of three dimensional models with two and three stable equilibria. For this purpose we construct computational algorithms and procedures for the detection and the refinement of points located on the separatrix manifolds that partition the phase space. The use of the so-called Radial Basis Function (RBF) Partition of Unity (PU) method is used to reconstruct the separatrices.