Basic feature quantities for analysis of periodic orbits in digital return maps

• Tada Naoki

  EE Department, Hosei University

• Saito Toshimichi

  EE Department, Hosei University

Abstract

This paper studies digital return maps defined on a set of points. Depending on parameters and initial states, the maps can generate a variety of periodic orbits. In order to analyze the periodic orbits, we present two feature quantities. The first and second quantities can characterize the plentifulness and a variety of periodic orbits, respectively. Constructing a feature plane of the two quantities, the dynamics of the map can be visualized. Using the feature quantities and feature plane, we investigate various periodic orbits in digital return maps derived from a basic class of cellular automata.

Journal

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 9 (1), 2-10, 2018

  The Institute of Electronics, Information and Communication Engineers

Keywords

• digital dynamical systems
• periodic orbits
• cellular automata

Details

• CRID: 1390001205345438208
• NII Article ID: 130006301356
• DOI: 10.1587/nolta.9.2
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/9/1/9_2/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed