  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 \cite{cavoretto11} and the
approximation scheme presented in \cite{cavoretto11,C-D-P-V}, 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 meshfree or meshless methods is used to
reconstruct the separatrices.
