Symmetry Breaking and Recovering in a System of n Hybridly Coupled Oscillators
Summary :
We consider a ring of n Rayleigh oscillators coupled hybridly. Using the symmetrical property of the system we demonstrate the degeneracy of the Hopf bifurcation of the equilibrium at the origin. The degeneracy implies the exstence and stability of the n-phase oscillation. We discuss some consequences of the perturbation of the symmetry. Then we study the case n = 3. We show the bifurcation diagram of the equilibria and of hte periodic solutions. Especially, we analyze the mechanism for the symmetry breaking bifurcation of the fully symmetric solution. We report and explain the occurrence of both chaotic attractors and repellors and show two types of symmetry recovering crisis they undergo.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.10 pp.1568-1574
- Publication Date
- 1996/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and its Applications (NOLTA))
- Category
- Nonlinear Circuits and Bifurcation
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Olivier PAPY, Hiroshi KAWAKAMI, "Symmetry Breaking and Recovering in a System of n Hybridly Coupled Oscillators" in IEICE TRANSACTIONS on Fundamentals,
vol. E79-A, no. 10, pp. 1568-1574, October 1996, doi: .
Abstract: We consider a ring of n Rayleigh oscillators coupled hybridly. Using the symmetrical property of the system we demonstrate the degeneracy of the Hopf bifurcation of the equilibrium at the origin. The degeneracy implies the exstence and stability of the n-phase oscillation. We discuss some consequences of the perturbation of the symmetry. Then we study the case n = 3. We show the bifurcation diagram of the equilibria and of hte periodic solutions. Especially, we analyze the mechanism for the symmetry breaking bifurcation of the fully symmetric solution. We report and explain the occurrence of both chaotic attractors and repellors and show two types of symmetry recovering crisis they undergo.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_10_1568/_p
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@ARTICLE{e79-a_10_1568,
author={Olivier PAPY, Hiroshi KAWAKAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Symmetry Breaking and Recovering in a System of n Hybridly Coupled Oscillators},
year={1996},
volume={E79-A},
number={10},
pages={1568-1574},
abstract={We consider a ring of n Rayleigh oscillators coupled hybridly. Using the symmetrical property of the system we demonstrate the degeneracy of the Hopf bifurcation of the equilibrium at the origin. The degeneracy implies the exstence and stability of the n-phase oscillation. We discuss some consequences of the perturbation of the symmetry. Then we study the case n = 3. We show the bifurcation diagram of the equilibria and of hte periodic solutions. Especially, we analyze the mechanism for the symmetry breaking bifurcation of the fully symmetric solution. We report and explain the occurrence of both chaotic attractors and repellors and show two types of symmetry recovering crisis they undergo.},
keywords={},
doi={},
ISSN={},
month={October},}
Copy
TY - JOUR
TI - Symmetry Breaking and Recovering in a System of n Hybridly Coupled Oscillators
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1568
EP - 1574
AU - Olivier PAPY
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 consider a ring of n Rayleigh oscillators coupled hybridly. Using the symmetrical property of the system we demonstrate the degeneracy of the Hopf bifurcation of the equilibrium at the origin. The degeneracy implies the exstence and stability of the n-phase oscillation. We discuss some consequences of the perturbation of the symmetry. Then we study the case n = 3. We show the bifurcation diagram of the equilibria and of hte periodic solutions. Especially, we analyze the mechanism for the symmetry breaking bifurcation of the fully symmetric solution. We report and explain the occurrence of both chaotic attractors and repellors and show two types of symmetry recovering crisis they undergo.
ER -
English
