The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Propomos sistemas constantes múltiplos por partes (ab. MPC) e consideramos fenômenos básicos: os MPCs 2-D, 3-D e 4-D exibem ciclo limite, caos de expansão de linha e caos de expansão de área, respectivamente. O lado direito da equação de estado é constante por partes, portanto, a dinâmica do sistema pode ser simplificada em um mapa de retorno linear por partes que pode ser expresso explicitamente. Para analisar o mapa de retorno linear por partes, introduzimos uma função de avaliação para o mapa de retorno linear por partes e fornecemos evidências teóricas para a geração de caos. Também os comportamentos caóticos são demonstrados em laboratório.
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Tadashi TSUBONE, Toshimichi SAITO, "Manifold Piecewise Constant Systems and Chaos" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 8, pp. 1619-1626, August 1999, doi: .
Abstract: We propose manifold piecewise constant systems (ab. MPC) and consider basic phenomena: the 2-D, 3-D and 4-D MPCs exhibit limit-cycle, line-expanding chaos and area-expanding chaos, respectively. The righthand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewise-linear return map which can be expressed explicitly. In order to analyze the piecewise-linear return map, we introduce an evaluation function for the piecewise-linear return map and give theoretical evidence for chaos generation. Also the chaotic behaviors are demonstrated in the laboratory.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_8_1619/_p
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@ARTICLE{e82-a_8_1619,
author={Tadashi TSUBONE, Toshimichi SAITO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Manifold Piecewise Constant Systems and Chaos},
year={1999},
volume={E82-A},
number={8},
pages={1619-1626},
abstract={We propose manifold piecewise constant systems (ab. MPC) and consider basic phenomena: the 2-D, 3-D and 4-D MPCs exhibit limit-cycle, line-expanding chaos and area-expanding chaos, respectively. The righthand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewise-linear return map which can be expressed explicitly. In order to analyze the piecewise-linear return map, we introduce an evaluation function for the piecewise-linear return map and give theoretical evidence for chaos generation. Also the chaotic behaviors are demonstrated in the laboratory.},
keywords={},
doi={},
ISSN={},
month={August},}
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TY - JOUR
TI - Manifold Piecewise Constant Systems and Chaos
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1619
EP - 1626
AU - Tadashi TSUBONE
AU - Toshimichi SAITO
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 1999
AB - We propose manifold piecewise constant systems (ab. MPC) and consider basic phenomena: the 2-D, 3-D and 4-D MPCs exhibit limit-cycle, line-expanding chaos and area-expanding chaos, respectively. The righthand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewise-linear return map which can be expressed explicitly. In order to analyze the piecewise-linear return map, we introduce an evaluation function for the piecewise-linear return map and give theoretical evidence for chaos generation. Also the chaotic behaviors are demonstrated in the laboratory.
ER -