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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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| Cite this article: |
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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.
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| Keywords:
05.45.-a
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Received: 28 December 2007
Published: 25 July 2008
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| PACS: |
05.45.-a
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(Nonlinear dynamics and chaos)
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[9] Thompson J M T et al 1986 Nonlinear Dynamics andChaos (New York: Wiley) p 72
[10] Lei Y M et al 2006 Chaos, Solitons Fractals 28 426 |
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