Bifurcations of Periodic Solutions in a Coupled Oscillator with Voltage Ports

Hiroyuki KITAJIMA; Yuji KATSUTA; Hiroshi KAWAKAMI

Bifurcations of Periodic Solutions in a Coupled Oscillator with Voltage Ports

Hiroyuki KITAJIMA, Yuji KATSUTA, Hiroshi KAWAKAMI

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In this paper, we study bifurcations of equilibrium points and periodic solutions observed in a resistively coupled oscillator with voltage ports. We classify equilibrium points and periodic solutions into four and eight different types, respectively, according to their symmetrical properties. By calculating D-type of branching sets (symmetry-breaking bifurcations) of equilibrium points and periodic solutions, we show that all types of equilibrium points and periodic solutions are systematically found. Possible oscillations in two coupled oscillators are presented by calculating Hopf bifurcation sets of equilibrium points. A parameter region in which chaotic oscillations exist is also shown by obtaining a cascade of period-doubling bifurcation sets.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.3 pp.476-482

Publication Date: 1998/03/25

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Category: Nonlinear Problems

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Hiroyuki KITAJIMA, Yuji KATSUTA, Hiroshi KAWAKAMI, "Bifurcations of Periodic Solutions in a Coupled Oscillator with Voltage Ports" in IEICE TRANSACTIONS on Fundamentals, vol. E81-A, no. 3, pp. 476-482, March 1998, doi: .
Abstract: In this paper, we study bifurcations of equilibrium points and periodic solutions observed in a resistively coupled oscillator with voltage ports. We classify equilibrium points and periodic solutions into four and eight different types, respectively, according to their symmetrical properties. By calculating D-type of branching sets (symmetry-breaking bifurcations) of equilibrium points and periodic solutions, we show that all types of equilibrium points and periodic solutions are systematically found. Possible oscillations in two coupled oscillators are presented by calculating Hopf bifurcation sets of equilibrium points. A parameter region in which chaotic oscillations exist is also shown by obtaining a cascade of period-doubling bifurcation sets.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e81-a_3_476/_p

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@ARTICLE{e81-a_3_476,
author={Hiroyuki KITAJIMA, Yuji KATSUTA, Hiroshi KAWAKAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Bifurcations of Periodic Solutions in a Coupled Oscillator with Voltage Ports},
year={1998},
volume={E81-A},
number={3},
pages={476-482},
abstract={In this paper, we study bifurcations of equilibrium points and periodic solutions observed in a resistively coupled oscillator with voltage ports. We classify equilibrium points and periodic solutions into four and eight different types, respectively, according to their symmetrical properties. By calculating D-type of branching sets (symmetry-breaking bifurcations) of equilibrium points and periodic solutions, we show that all types of equilibrium points and periodic solutions are systematically found. Possible oscillations in two coupled oscillators are presented by calculating Hopf bifurcation sets of equilibrium points. A parameter region in which chaotic oscillations exist is also shown by obtaining a cascade of period-doubling bifurcation sets.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - Bifurcations of Periodic Solutions in a Coupled Oscillator with Voltage Ports
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 476
EP - 482
AU - Hiroyuki KITAJIMA
AU - Yuji KATSUTA
AU - Hiroshi KAWAKAMI
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1998
AB - In this paper, we study bifurcations of equilibrium points and periodic solutions observed in a resistively coupled oscillator with voltage ports. We classify equilibrium points and periodic solutions into four and eight different types, respectively, according to their symmetrical properties. By calculating D-type of branching sets (symmetry-breaking bifurcations) of equilibrium points and periodic solutions, we show that all types of equilibrium points and periodic solutions are systematically found. Possible oscillations in two coupled oscillators are presented by calculating Hopf bifurcation sets of equilibrium points. A parameter region in which chaotic oscillations exist is also shown by obtaining a cascade of period-doubling bifurcation sets.
ER -