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

TitleMeshless partition of unity method for attraction basins of periodic orbits: Fast detection of separatrix points
Publication TypeJournal Article
Year of Publication2018
AuthorsDe Rossi, A, Perracchione, E, Venturino, E
JournalDolomites Research Notes on Approximation
Volume11
Issue2
Pagination15-22
Date Published01/2018
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number2035-6803
Abstract

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.

URLhttp://drna.padovauniversitypress.it/2018/2/3