Codimension Two Bifurcation Observed in a Phase Converter Circuit

Hiroyuki KITAJIMA; Tetsuya YOSHINAGA; Hiroshi KAWAKAMI

Codimension Two Bifurcation Observed in a Phase Converter Circuit

Hiroyuki KITAJIMA, Tetsuya YOSHINAGA, Hiroshi KAWAKAMI

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We investigate bifurcations of the periodic solution observed in a phase converter circuit. The system equations can be considered as a nonlinear coupled system with Duffing's equation and an equation describing a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. From numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Pericdic solutions generated by these bifurcations become chaotic states through a cascade of codimension three bifurcations which are intersections of D-type of branchings and period-doubling bifurcations.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.10 pp.1563-1567

Publication Date: 1996/10/25

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Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications (NOLTA))

Category: Nonlinear Circuits and Bifurcation

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Hiroyuki KITAJIMA, Tetsuya YOSHINAGA, Hiroshi KAWAKAMI, "Codimension Two Bifurcation Observed in a Phase Converter Circuit" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 10, pp. 1563-1567, October 1996, doi: .
Abstract: We investigate bifurcations of the periodic solution observed in a phase converter circuit. The system equations can be considered as a nonlinear coupled system with Duffing's equation and an equation describing a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. From numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Pericdic solutions generated by these bifurcations become chaotic states through a cascade of codimension three bifurcations which are intersections of D-type of branchings and period-doubling bifurcations.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_10_1563/_p

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@ARTICLE{e79-a_10_1563,
author={Hiroyuki KITAJIMA, Tetsuya YOSHINAGA, Hiroshi KAWAKAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Codimension Two Bifurcation Observed in a Phase Converter Circuit},
year={1996},
volume={E79-A},
number={10},
pages={1563-1567},
abstract={We investigate bifurcations of the periodic solution observed in a phase converter circuit. The system equations can be considered as a nonlinear coupled system with Duffing's equation and an equation describing a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. From numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Pericdic solutions generated by these bifurcations become chaotic states through a cascade of codimension three bifurcations which are intersections of D-type of branchings and period-doubling bifurcations.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - Codimension Two Bifurcation Observed in a Phase Converter Circuit
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1563
EP - 1567
AU - Hiroyuki KITAJIMA
AU - Tetsuya YOSHINAGA
AU - Hiroshi KAWAKAMI
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1996
AB - We investigate bifurcations of the periodic solution observed in a phase converter circuit. The system equations can be considered as a nonlinear coupled system with Duffing's equation and an equation describing a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. From numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Pericdic solutions generated by these bifurcations become chaotic states through a cascade of codimension three bifurcations which are intersections of D-type of branchings and period-doubling bifurcations.
ER -