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

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.

De Rossi A., Perracchione E., Venturino E. (2018) "Meshless partition of unity method for attraction basins of periodic orbits: Fast detection of separatrix points " Dolomites Research Notes on Approximation, 11(2), 15-22. DOI: 10.14658/PUPJ-DRNA-2018-2-3  
Year of Publication
2018
Journal
Dolomites Research Notes on Approximation
Volume
11
Issue Number
2
Start Page
15
Last Page
22
Date Published
01/2018
ISSN Number
2035-6803
Serial Article Number
3
DOI
10.14658/PUPJ-DRNA-2018-2-3
Issue
Section
SpecialIssue