Chaotic Phenomena in a Circuit with a Negative Resistance and an ldeal Switch of Diodes

Naohiko INABA; Toshimichi SAITO; Shinsaku MORI

Chaotic Phenomena in a Circuit with a Negative Resistance and an ldeal Switch of Diodes

Naohiko INABA, Toshimichi SAITO, Shinsaku MORI

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It is known that the modified van der Poloscillator proposed by Shinriki et al. can exhibit various interesting phenomena such as a period-doubling-bifurcation, chaos, windows, and a Double Scroll like attractor. But the mechanism of the generation of such phenomena has not yet been explained and cleared. In this paper, it is shown that the phenomena generated in the Shinrikis' circuit could be well explained by a simplified model which we hereafter call as the Ideal System. Here the idealization means that the element of diodes in the circuit operates as an ideal switch. The Ideal System is extremely simple because it contains 3 reactance elements, one linear negative coductance and only one nonlinear element constructed from diodes where the operation of such nonlinear element is very simple. The advantages of using the Ideal System to analyze the mechanism of chaos are as follows: Poincaré map could be derived strictly as a 1-dimensional discrete map from this model and from this obtained Poincaré map, the phenomena could be well explained. Moreover, the theoretical results are verified in the circuit experiments. The Ideal System makes clear the mechanism of chaos gonerated in the circuit.

Publication: IEICE TRANSACTIONS on transactions Vol.E70-E No.8 pp.744-754

Publication Date: 1987/08/25

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Type of Manuscript: PAPER

Category: Nonlinear Problems

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Naohiko INABA
Toshimichi SAITO
Shinsaku MORI

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Naohiko INABA, Toshimichi SAITO, Shinsaku MORI, "Chaotic Phenomena in a Circuit with a Negative Resistance and an ldeal Switch of Diodes" in IEICE TRANSACTIONS on transactions, vol. E70-E, no. 8, pp. 744-754, August 1987, doi: .
Abstract: It is known that the modified van der Poloscillator proposed by Shinriki et al. can exhibit various interesting phenomena such as a period-doubling-bifurcation, chaos, windows, and a Double Scroll like attractor. But the mechanism of the generation of such phenomena has not yet been explained and cleared. In this paper, it is shown that the phenomena generated in the Shinrikis' circuit could be well explained by a simplified model which we hereafter call as the Ideal System. Here the idealization means that the element of diodes in the circuit operates as an ideal switch. The Ideal System is extremely simple because it contains 3 reactance elements, one linear negative coductance and only one nonlinear element constructed from diodes where the operation of such nonlinear element is very simple. The advantages of using the Ideal System to analyze the mechanism of chaos are as follows: Poincaré map could be derived strictly as a 1-dimensional discrete map from this model and from this obtained Poincaré map, the phenomena could be well explained. Moreover, the theoretical results are verified in the circuit experiments. The Ideal System makes clear the mechanism of chaos gonerated in the circuit.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e70-e_8_744/_p

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@ARTICLE{e70-e_8_744,
author={Naohiko INABA, Toshimichi SAITO, Shinsaku MORI, },
journal={IEICE TRANSACTIONS on transactions},
title={Chaotic Phenomena in a Circuit with a Negative Resistance and an ldeal Switch of Diodes},
year={1987},
volume={E70-E},
number={8},
pages={744-754},
abstract={It is known that the modified van der Poloscillator proposed by Shinriki et al. can exhibit various interesting phenomena such as a period-doubling-bifurcation, chaos, windows, and a Double Scroll like attractor. But the mechanism of the generation of such phenomena has not yet been explained and cleared. In this paper, it is shown that the phenomena generated in the Shinrikis' circuit could be well explained by a simplified model which we hereafter call as the Ideal System. Here the idealization means that the element of diodes in the circuit operates as an ideal switch. The Ideal System is extremely simple because it contains 3 reactance elements, one linear negative coductance and only one nonlinear element constructed from diodes where the operation of such nonlinear element is very simple. The advantages of using the Ideal System to analyze the mechanism of chaos are as follows: Poincaré map could be derived strictly as a 1-dimensional discrete map from this model and from this obtained Poincaré map, the phenomena could be well explained. Moreover, the theoretical results are verified in the circuit experiments. The Ideal System makes clear the mechanism of chaos gonerated in the circuit.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - Chaotic Phenomena in a Circuit with a Negative Resistance and an ldeal Switch of Diodes
T2 - IEICE TRANSACTIONS on transactions
SP - 744
EP - 754
AU - Naohiko INABA
AU - Toshimichi SAITO
AU - Shinsaku MORI
PY - 1987
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E70-E
IS - 8
JA - IEICE TRANSACTIONS on transactions
Y1 - August 1987
AB - It is known that the modified van der Poloscillator proposed by Shinriki et al. can exhibit various interesting phenomena such as a period-doubling-bifurcation, chaos, windows, and a Double Scroll like attractor. But the mechanism of the generation of such phenomena has not yet been explained and cleared. In this paper, it is shown that the phenomena generated in the Shinrikis' circuit could be well explained by a simplified model which we hereafter call as the Ideal System. Here the idealization means that the element of diodes in the circuit operates as an ideal switch. The Ideal System is extremely simple because it contains 3 reactance elements, one linear negative coductance and only one nonlinear element constructed from diodes where the operation of such nonlinear element is very simple. The advantages of using the Ideal System to analyze the mechanism of chaos are as follows: Poincaré map could be derived strictly as a 1-dimensional discrete map from this model and from this obtained Poincaré map, the phenomena could be well explained. Moreover, the theoretical results are verified in the circuit experiments. The Ideal System makes clear the mechanism of chaos gonerated in the circuit.
ER -