A topological computation approach to the interior crisis bifurcation

• Kokubu Hiroshi

  Department of Mathematics/JST-CREST, Kyoto University

• Oka Hiroe

  Department of Applied Mathematics and Informatics Faculty of Science and Technology, Ryukoku University

Abstract

We study the interior crisis bifurcation from the viewpoint of the graph-based topological computation developed in [2]. We give a new formulation of the interior crisis bifurcation in terms of a change of the attractor-repeller decompositions of the dynamics, and prove that the attractor before the crisis disappears by creating a chain connecting orbit to the repeller at the moment of the interior crisis. As an illustration, we discuss the interior crisis bifurcation in the Ikeda map.

Journal

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 4 (1), 97-103, 2013

  The Institute of Electronics, Information and Communication Engineers

Keywords

• dynamical system
• bifurcation
• interior crisis
• Morse decomposition
• Conley index
• topological computation

Details

• CRID: 1390282680322039296
• NII Article ID: 130003375415
• DOI: 10.1587/nolta.4.97
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/4/1/4_97/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed