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论文:2015,Vol:33,Issue(1):88-92 |
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引用本文： |
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张莹, 李爽. 重访Duffing系统中的对称破裂分岔与激变[J]. 西北工业大学学报 |
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Zhang Ying, Li Shuang. Revisiting of SB (Symmetry Breaking) Bifurcation and Crisis in Duffing System[J]. Northwestern polytechnical university |
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| 重访Duffing系统中的对称破裂分岔与激变 |
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| 张莹1, 李爽2 |
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1. 西北工业大学应用数学系, 陕西西安 710072;
2. 西安财经学院统计学院, 陕西西安 710100 |
| 摘要: |
| 借Duffing系统在简谐激励下发生的对称破裂分岔与激变的实例分析,推介对称系统非线性动力学现象的特色及其研究对策;解释了混沌鞍在混沌动力学分析中的作用。研究表明:周期解的对称破裂分岔只需通过一次鞍结分岔就可直接实现。而混沌吸引子的对称破裂激变往往需要通过边界激变、内部激变与吸引子融合激变等组合手段方能实现。 |
| 关键词:
对称破裂(SB)分岔
边界激变
内部激变
吸引子融合激变
TLE
混沌鞍
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| Revisiting of SB (Symmetry Breaking) Bifurcation and Crisis in Duffing System |
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| Zhang Ying1, Li Shuang2 |
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1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2. School of Statistics, Xi'an University of Finance & Economics, Xi'an 710100, China |
| Abstract: |
| Bifurcation or Crisis stands for abrupt change of regular motion or chaotic motion due to minute deviation of a key parameter in nonlinear systems. On the basis of observing SB bifurcation and crises in Duffing systems, we introduce the main features of these nonlinear phenomena and ways to deal with these problems. We find that SB bifurcations can be simply realized by the way of saddle-node bifurcation, while SB crises can only be realized by the way of a combination of boundary crisis, interior crisis, and attractor merging crisis. Besides, the important role of chaotic saddle in analysis of SB crisis is explained in simple terms. |
| Key words:
bifurcation (mathematics)
chaos theory
differential equations
nonlinear systems
Top Lyapunov exponent
attractor emerging crisis
boundary crisis
chaotic saddle
interior crisis
SB (Symmetry Breaking)
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| 收稿日期: 2014-05-08
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金(11472212、11302171)与中央高校基本科研业务费专项资金(3102014JCQ01080)资助 |
| 通讯作者:
Email： |
| 作者简介: 张莹(1981-),女,西北工业大学讲师,主要从事随机非线性动力学研究。
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| 作者相关文章 |
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| 张莹 在本刊中的所有文章 |
| 李爽 在本刊中的所有文章 |
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参考文献: |
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[1] Fang T, Dowell E H. Numerical Simulations of Periodic and Chaotic Responses in a Stable Duffing System[J]. International Journal of Nonlinear Mechanics, 1987, 22(5):401-425
[2] 方同.有关混沌及其控制与同步的一些理解[J].振动工程学报, 2007, 20(5):447-452 Fang T. Understanding of Chaos Together with Its Control and Synchronization[J]. Journal of Vibration Engineering, 2007, 20(5):447-452(in Chinese)
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[7] Zhang Y, Rossetto B, Xu W, Yue XL, Fang T. Roles of Chaotic Saddle and Basin of Attraction in Bifurcation and Crisis Analysis[J]. International Journal of Bifurcation and Chaos, 2011, 21(3):903-915 |
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