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 solvedby means of meshfree interpolation tools. We propose a novel approach to calculate separatrix manifoldsby detecting points via an efficient bisection-like scheme. Such data are then interpolated by means ofthe implicit Partition of Unity (PU) method. The detection algorithm works for dynamical systems of twoequations, speeds up the computational time of the previously studied routines and allows the treatmentof periodic orbits.