A Complete Bifurcation Set of Chenciner Bubbles
Summary :
This study investigates quasiperiodic bifurcations generated in a coupled delayed logistic map. Since a delayed logistic map generates an invariant closed curve (ICC), a coupled delayed logistic map exhibits an invariant torus (IT). In a parameter region generating IT, ICC-generating regions extend in many directions like a web. This bifurcation structure is called an Arnol'd resonance web. In this study, we investigate the bifurcation structure of Chenciner bubbles, which are complete synchronization regions in the parameter space, and illustrate a complete bifurcation set for one of Chenciner bubbles. The bifurcation boundary of the Chenciner bubbles is surrounded by saddle-node bifurcation curves and Neimark-Sacker bifurcation curves.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.12 pp.2719-2722
- Publication Date
- 2015/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E98.A.2719
- Type of Manuscript
- LETTER
- Category
- Nonlinear Problems
Authors
Munehisa SEKIKAWA
Utsunomiya University
Naohiko INABA
Meiji University
Keyword
Latest Issue
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Munehisa SEKIKAWA, Naohiko INABA, "A Complete Bifurcation Set of Chenciner Bubbles" in IEICE TRANSACTIONS on Fundamentals,
vol. E98-A, no. 12, pp. 2719-2722, December 2015, doi: 10.1587/transfun.E98.A.2719.
Abstract: This study investigates quasiperiodic bifurcations generated in a coupled delayed logistic map. Since a delayed logistic map generates an invariant closed curve (ICC), a coupled delayed logistic map exhibits an invariant torus (IT). In a parameter region generating IT, ICC-generating regions extend in many directions like a web. This bifurcation structure is called an Arnol'd resonance web. In this study, we investigate the bifurcation structure of Chenciner bubbles, which are complete synchronization regions in the parameter space, and illustrate a complete bifurcation set for one of Chenciner bubbles. The bifurcation boundary of the Chenciner bubbles is surrounded by saddle-node bifurcation curves and Neimark-Sacker bifurcation curves.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.2719/_p
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@ARTICLE{e98-a_12_2719,
author={Munehisa SEKIKAWA, Naohiko INABA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Complete Bifurcation Set of Chenciner Bubbles},
year={2015},
volume={E98-A},
number={12},
pages={2719-2722},
abstract={This study investigates quasiperiodic bifurcations generated in a coupled delayed logistic map. Since a delayed logistic map generates an invariant closed curve (ICC), a coupled delayed logistic map exhibits an invariant torus (IT). In a parameter region generating IT, ICC-generating regions extend in many directions like a web. This bifurcation structure is called an Arnol'd resonance web. In this study, we investigate the bifurcation structure of Chenciner bubbles, which are complete synchronization regions in the parameter space, and illustrate a complete bifurcation set for one of Chenciner bubbles. The bifurcation boundary of the Chenciner bubbles is surrounded by saddle-node bifurcation curves and Neimark-Sacker bifurcation curves.},
keywords={},
doi={10.1587/transfun.E98.A.2719},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - A Complete Bifurcation Set of Chenciner Bubbles
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2719
EP - 2722
AU - Munehisa SEKIKAWA
AU - Naohiko INABA
PY - 2015
DO - 10.1587/transfun.E98.A.2719
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2015
AB - This study investigates quasiperiodic bifurcations generated in a coupled delayed logistic map. Since a delayed logistic map generates an invariant closed curve (ICC), a coupled delayed logistic map exhibits an invariant torus (IT). In a parameter region generating IT, ICC-generating regions extend in many directions like a web. This bifurcation structure is called an Arnol'd resonance web. In this study, we investigate the bifurcation structure of Chenciner bubbles, which are complete synchronization regions in the parameter space, and illustrate a complete bifurcation set for one of Chenciner bubbles. The bifurcation boundary of the Chenciner bubbles is surrounded by saddle-node bifurcation curves and Neimark-Sacker bifurcation curves.
ER -
English
