Chaos and Related Bifurcation Phenomena from a Simple Hysteresis Network
Summary :
This paper proposes a tool to analyze complicated phenomena from a simple hysteresis network. The simple hysteresis network is described by a piecewise liner ordinal differential equation and has only two parameters: self feedback and DC team. Then this simple system exhibits various kinds of attractors: stable equilibria, periodic orbits, tori and chaos. In order to perform the numerical analysis, we derive return map and propose a fast calculation algorithm for the return map and its Lyapunov exponents based on the exact solutions. Using this algorithm, we have clarified chaos generation and related bifurcation phenomena. Also, we give theoretical formula that give fundamental bifurcation set.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.3 pp.402-414
- Publication Date
- 1996/03/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Nonlinear Problems
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Kenya JIN'NO, "Chaos and Related Bifurcation Phenomena from a Simple Hysteresis Network" in IEICE TRANSACTIONS on Fundamentals,
vol. E79-A, no. 3, pp. 402-414, March 1996, doi: .
Abstract: This paper proposes a tool to analyze complicated phenomena from a simple hysteresis network. The simple hysteresis network is described by a piecewise liner ordinal differential equation and has only two parameters: self feedback and DC team. Then this simple system exhibits various kinds of attractors: stable equilibria, periodic orbits, tori and chaos. In order to perform the numerical analysis, we derive return map and propose a fast calculation algorithm for the return map and its Lyapunov exponents based on the exact solutions. Using this algorithm, we have clarified chaos generation and related bifurcation phenomena. Also, we give theoretical formula that give fundamental bifurcation set.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_3_402/_p
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@ARTICLE{e79-a_3_402,
author={Kenya JIN'NO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Chaos and Related Bifurcation Phenomena from a Simple Hysteresis Network},
year={1996},
volume={E79-A},
number={3},
pages={402-414},
abstract={This paper proposes a tool to analyze complicated phenomena from a simple hysteresis network. The simple hysteresis network is described by a piecewise liner ordinal differential equation and has only two parameters: self feedback and DC team. Then this simple system exhibits various kinds of attractors: stable equilibria, periodic orbits, tori and chaos. In order to perform the numerical analysis, we derive return map and propose a fast calculation algorithm for the return map and its Lyapunov exponents based on the exact solutions. Using this algorithm, we have clarified chaos generation and related bifurcation phenomena. Also, we give theoretical formula that give fundamental bifurcation set.},
keywords={},
doi={},
ISSN={},
month={March},}
Copy
TY - JOUR
TI - Chaos and Related Bifurcation Phenomena from a Simple Hysteresis Network
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 402
EP - 414
AU - Kenya JIN'NO
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1996
AB - This paper proposes a tool to analyze complicated phenomena from a simple hysteresis network. The simple hysteresis network is described by a piecewise liner ordinal differential equation and has only two parameters: self feedback and DC team. Then this simple system exhibits various kinds of attractors: stable equilibria, periodic orbits, tori and chaos. In order to perform the numerical analysis, we derive return map and propose a fast calculation algorithm for the return map and its Lyapunov exponents based on the exact solutions. Using this algorithm, we have clarified chaos generation and related bifurcation phenomena. Also, we give theoretical formula that give fundamental bifurcation set.
ER -
English
