On the sighting of unicorns: A variational approach to computing invariant sets in dynamical systems

Oliver Junge, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We propose to compute approximations to invariant sets in dynamical systems by minimizing an appropriate distance between a suitably selected finite set of points and its image under the dynamics. We demonstrate, through computational experiments, that this approach can successfully converge to approximations of (maximal) invariant sets of arbitrary topology, dimension, and stability, such as, e.g., saddle type invariant sets with complicated dynamics. We further propose to extend this approach by adding a Lennard-Jones type potential term to the objective function, which yields more evenly distributed approximating finite point sets, and illustrate the procedure through corresponding numerical experiments.

Original languageEnglish (US)
Article number063102
JournalChaos
Volume27
Issue number6
DOIs
StatePublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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