Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
Special Section on Recent Progress in Nonlinear Theory and Its Applications
Basic feature quantities for analysis of periodic orbits in digital return maps
Naoki TadaToshimichi Saito
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2018 Volume 9 Issue 1 Pages 2-10

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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.

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© 2018 The Institute of Electronics, Information and Communication Engineers
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