Bifurcation Set of a Modelled Parallel Blower System
Summary :
Global dynamic behavior particularly the bifurcation of periodic orbits of a parallel blower system is studied using a piecewise linear model and the one-dimensional map defined by the Poincare map. First several analytical tools are presented to numerically study the bifurcation process particularly the bifurcation point of the fixed point of the Poincare map. Using two bifurcation diagrams and a bifurcation set, it is shown how periodic orbits bifurcate and leads to chaotic state. It is also shown that the homoclinic bifurcations occur in some parameter regions and that the Li & Yorke conditions of the chaotic state hold in the parameter region which is included in the one where the homoclinic bifurcation occurs. Together with the above, the stable and unstable manifolds of a saddle closed orbit is illustrated and the existence of the homoclinic points is shown.
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- IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.3 pp.299-309
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- 1993/03/25
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- Special Section PAPER (Special Section on the 5th Karuizawa Workshop on Circuits and Systems)
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Hideaki OKAZAKI, Tomoyuki UWABA, Hideo NAKANO, Takehiko KAWASE, "Bifurcation Set of a Modelled Parallel Blower System" in IEICE TRANSACTIONS on Fundamentals,
vol. E76-A, no. 3, pp. 299-309, March 1993, doi: .
Abstract: Global dynamic behavior particularly the bifurcation of periodic orbits of a parallel blower system is studied using a piecewise linear model and the one-dimensional map defined by the Poincare map. First several analytical tools are presented to numerically study the bifurcation process particularly the bifurcation point of the fixed point of the Poincare map. Using two bifurcation diagrams and a bifurcation set, it is shown how periodic orbits bifurcate and leads to chaotic state. It is also shown that the homoclinic bifurcations occur in some parameter regions and that the Li & Yorke conditions of the chaotic state hold in the parameter region which is included in the one where the homoclinic bifurcation occurs. Together with the above, the stable and unstable manifolds of a saddle closed orbit is illustrated and the existence of the homoclinic points is shown.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e76-a_3_299/_p
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@ARTICLE{e76-a_3_299,
author={Hideaki OKAZAKI, Tomoyuki UWABA, Hideo NAKANO, Takehiko KAWASE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Bifurcation Set of a Modelled Parallel Blower System},
year={1993},
volume={E76-A},
number={3},
pages={299-309},
abstract={Global dynamic behavior particularly the bifurcation of periodic orbits of a parallel blower system is studied using a piecewise linear model and the one-dimensional map defined by the Poincare map. First several analytical tools are presented to numerically study the bifurcation process particularly the bifurcation point of the fixed point of the Poincare map. Using two bifurcation diagrams and a bifurcation set, it is shown how periodic orbits bifurcate and leads to chaotic state. It is also shown that the homoclinic bifurcations occur in some parameter regions and that the Li & Yorke conditions of the chaotic state hold in the parameter region which is included in the one where the homoclinic bifurcation occurs. Together with the above, the stable and unstable manifolds of a saddle closed orbit is illustrated and the existence of the homoclinic points is shown.},
keywords={},
doi={},
ISSN={},
month={March},}
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TY - JOUR
TI - Bifurcation Set of a Modelled Parallel Blower System
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 299
EP - 309
AU - Hideaki OKAZAKI
AU - Tomoyuki UWABA
AU - Hideo NAKANO
AU - Takehiko KAWASE
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1993
AB - Global dynamic behavior particularly the bifurcation of periodic orbits of a parallel blower system is studied using a piecewise linear model and the one-dimensional map defined by the Poincare map. First several analytical tools are presented to numerically study the bifurcation process particularly the bifurcation point of the fixed point of the Poincare map. Using two bifurcation diagrams and a bifurcation set, it is shown how periodic orbits bifurcate and leads to chaotic state. It is also shown that the homoclinic bifurcations occur in some parameter regions and that the Li & Yorke conditions of the chaotic state hold in the parameter region which is included in the one where the homoclinic bifurcation occurs. Together with the above, the stable and unstable manifolds of a saddle closed orbit is illustrated and the existence of the homoclinic points is shown.
ER -
English
