Attractors in an Eventually Bounded Circuit

Makoto ITOH; Sanemitsu HAYASHI

Attractors in an Eventually Bounded Circuit

Makoto ITOH, Sanemitsu HAYASHI

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Our primary purpose of this paper is to study attractors and bifurcation phenomenon appearing in an eventually bounded circuit. The secondary purpose is to demonstrate the results obtained from the instruments which display Lorenz maps, Poincaré maps and cross sections of attractors on a synchroscope. The above mentioned circuit contains two non-linear resistors and is written as 3 first order differential equations. Experimental observations show:
(a) maximum number of the attractors in three.
(b) maximum number of the stable limit cycles is three.
(c) maximum number of the chaotic attractor is two.
Observed bifurcations are:
(a) Hopf bifurcation,
(b) period doubling bifurcation,
(c) periodic window.
Furthermore, we examined the Feigenbaum constant δ experimentally and estimated it at 4.67.

Publication: IEICE TRANSACTIONS on transactions Vol.E71-E No.8 pp.750-758

Publication Date: 1988/08/25

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Type of Manuscript: PAPER

Category: Nonlinear Problems

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Makoto ITOH
Sanemitsu HAYASHI

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Makoto ITOH, Sanemitsu HAYASHI, "Attractors in an Eventually Bounded Circuit" in IEICE TRANSACTIONS on transactions, vol. E71-E, no. 8, pp. 750-758, August 1988, doi: .
Abstract: Our primary purpose of this paper is to study attractors and bifurcation phenomenon appearing in an eventually bounded circuit. The secondary purpose is to demonstrate the results obtained from the instruments which display Lorenz maps, Poincaré maps and cross sections of attractors on a synchroscope. The above mentioned circuit contains two non-linear resistors and is written as 3 first order differential equations. Experimental observations show:
(a) maximum number of the attractors in three.
(b) maximum number of the stable limit cycles is three.
(c) maximum number of the chaotic attractor is two.
Observed bifurcations are:
(a) Hopf bifurcation,
(b) period doubling bifurcation,
(c) periodic window.
Furthermore, we examined the Feigenbaum constant δ experimentally and estimated it at 4.67.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e71-e_8_750/_p

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@ARTICLE{e71-e_8_750,
author={Makoto ITOH, Sanemitsu HAYASHI, },
journal={IEICE TRANSACTIONS on transactions},
title={Attractors in an Eventually Bounded Circuit},
year={1988},
volume={E71-E},
number={8},
pages={750-758},
abstract={Our primary purpose of this paper is to study attractors and bifurcation phenomenon appearing in an eventually bounded circuit. The secondary purpose is to demonstrate the results obtained from the instruments which display Lorenz maps, Poincaré maps and cross sections of attractors on a synchroscope. The above mentioned circuit contains two non-linear resistors and is written as 3 first order differential equations. Experimental observations show:
(a) maximum number of the attractors in three.
(b) maximum number of the stable limit cycles is three.
(c) maximum number of the chaotic attractor is two.
Observed bifurcations are:
(a) Hopf bifurcation,
(b) period doubling bifurcation,
(c) periodic window.
Furthermore, we examined the Feigenbaum constant δ experimentally and estimated it at 4.67.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - Attractors in an Eventually Bounded Circuit
T2 - IEICE TRANSACTIONS on transactions
SP - 750
EP - 758
AU - Makoto ITOH
AU - Sanemitsu HAYASHI
PY - 1988
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E71-E
IS - 8
JA - IEICE TRANSACTIONS on transactions
Y1 - August 1988
AB - Our primary purpose of this paper is to study attractors and bifurcation phenomenon appearing in an eventually bounded circuit. The secondary purpose is to demonstrate the results obtained from the instruments which display Lorenz maps, Poincaré maps and cross sections of attractors on a synchroscope. The above mentioned circuit contains two non-linear resistors and is written as 3 first order differential equations. Experimental observations show:
(a) maximum number of the attractors in three.
(b) maximum number of the stable limit cycles is three.
(c) maximum number of the chaotic attractor is two.
Observed bifurcations are:
(a) Hopf bifurcation,
(b) period doubling bifurcation,
(c) periodic window.
Furthermore, we examined the Feigenbaum constant δ experimentally and estimated it at 4.67.
ER -