Chin. Phys. Lett.  2008, Vol. 25 Issue (8): 2809-2811    DOI:
Original Articles |
Insight into Phenomena of Symmetry Breaking Bifurcation
FANG Tong1, ZHANG Ying2
1Department of Engineering Mechanics, Northwestern Polytechnical University, Xian 7100722Department of Applied Mathematics, Northwestern Polytechnical University, Xian 710072
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FANG Tong, ZHANG Ying 2008 Chin. Phys. Lett. 25 2809-2811
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Abstract We show that symmetry-breaking (SB) bifurcation is just a transition of different forms of symmetry, while still preserving system's symmetry. SB bifurcation always associates with a periodic saddle-node bifurcation, identifiable by a zero maximum of the top Lyapunov exponent of the system. In addition, we show a significant phase portrait of a newly born periodic saddle and its stable and unstable invariant manifolds, together with their neighbouring flow pattern of Poincaré mapping points just after the periodic saddle-node bifurcation, thus gaining an insight into the mechanism of SB bifurcation.
Keywords: 05.45.-a     
Received: 28 December 2007      Published: 25 July 2008
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
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https://cpl.iphy.ac.cn/       OR      https://cpl.iphy.ac.cn/Y2008/V25/I8/02809
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FANG Tong
ZHANG Ying
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[2] Sunner T et al 1993 Int. J. Bifur. Chaos 3399
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