Construction of local Lyapunov functions around non-hyperbolic equilibria by verified numerics for two dimensional cases

• Terasaka Gen

  JR East Information Systems Company

• Nakamura Masao

  Graduate School of Informatics and Engineering, The University of Electro-Communications

• Nitta Koki

  Graduate School of Informatics and Engineering, The University of Electro-Communications

• Yamamoto Nobito

  Graduate School of Informatics and Engineering, The University of Electro-Communications

Abstract

Numerical verification methods are proposed in order to construct local Lyapunov functions around non-hyperbolic equilibria of dynamical systems described by ODEs in two dimensional space. The normal form theory in dynamical systems gives basic ideas of these methods. To prove negative definiteness of polynomials of higher degree than two, a new theorem on interval arithmetic is also proposed.

Journal

• JSIAM Letters

  JSIAM Letters 12 (0), 37-40, 2020

  The Japan Society for Industrial and Applied Mathematics

Keywords

• numerical verification
• dynamical systems
• Lyapunov functions
• non-hyperbolic equilibria

Details

• CRID: 1390848250130871296
• NII Article ID: 130007879242
• DOI: 10.14495/jsiaml.12.37
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/12/0/12_37/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed