Some remarks on numerical verification of closed orbits in dynamical systems

• Hiwaki Tomohiro

  The University of Electro-Communications

• Yamamoto Nobito

  The University of Electro-Communications

Abstract

We consider numerical verification methods for existence of a closed orbit in a dynamical system which is described by ODEs. Besides Zgliczynski's method using Poincaré map, the authors proposed a method of verification for closed orbits and their time period. In this paper, we derive a relationship between our method and one of bordering methods which gives some explanation of superiority of this bordering.

Journal

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 6 (3), 397-403, 2015

  The Institute of Electronics, Information and Communication Engineers

Keywords

• numerical verification
• dynamical system
• ODEs
• closed orbit
• Poncaré map
• bordering condition

Details

• CRID: 1390001205345483904
• NII Article ID: 130005085582
• DOI: 10.1587/nolta.6.397
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/6/3/6_397/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed