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In this paper we consider the problem of reconstructing separatrices indynamical systems. In particular, here we aim at partitioning the domainapproximating the boundaries of the basins of attraction of different stableequilibria. We start from the 2D case sketched in \cite{cavoretto11} and theapproximation scheme presented in \cite{cavoretto11,C-D-P-V}, and then weextend the reconstruction scheme of separatrices in the cases of threedimensional models with two and three stable equilibria. For this purpose weconstruct computational algorithms and procedures for the detection and therefinement of points located on the separatrix manifolds that partition thephase space. The use of the so-called meshfree or meshless methods is used toreconstruct the separatrices.

Graphical representation of separatrices of attraction basins in two and three dimensional dynamical systems