Meshless partition of unity method for attraction basins of periodic orbits: Fast detection of separatrix points

Given a dynamical system, the problem of reconstructing the attraction basins can effectively be solved by means of meshfree interpolation tools. We propose a novel approach to calculate separatrix manifolds by detecting points via an efficient bisection-like scheme. Such data are then interpolated by means of the implicit Partition of Unity (PU) method. The detection algorithm works for dynamical systems of two equations, speeds up the computational time of the previously studied routines and allows the treatment of periodic orbits.