| SD振子中内部激变现象的研究 |
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| 引用本文： | 王建华,张晓燕,洪灵. SD振子中内部激变现象的研究[J]. 动力学与控制学报, 2011, 9(4): 331-336 |
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| 作者姓名： | 王建华 张晓燕 洪灵 |
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| 作者单位： | 西安交通大学强度与振动国家重点实验室,西安,710049 |
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| 基金项目： | 国家自然科学基金资助项目(10772140,10872155) |
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| 摘 要： | 应用广义胞映射图论方法(GCMD)研究SD(smooth and discontinuous systems)振子的内部激变现象,通过对SD常微分方程系统的全局分析发现周期解通向混沌的内部激变现象是由于周期吸引子与在其吸引域内部的混沌鞍碰撞产生的,混沌鞍是胞空间中的瞬态自循环胞集,周期吸引子与混沌鞍发生碰撞后,混沌鞍转...
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| 关 键 词： | 广义胞映射图论方法 内部激变 盒子维数 混沌鞍 |
| 收稿时间： | 2010-12-10 |
| 修稿时间： | 2011-07-07 |
Study of the interior crisis in SD oscillator |
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| Wang Jianhu,Zhang Xiaoyan and Hong Ling. Study of the interior crisis in SD oscillator[J]. Journal of Dynamics and Control, 2011, 9(4): 331-336 |
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| Authors: | Wang Jianhu Zhang Xiaoyan Hong Ling |
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| Affiliation: | Wang Jianhua Zhang Xiaoyan Hong Ling ( Xi＇ an Jiao Tong university, State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi＇ an 710049, China) |
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| Abstract: | The interior crisis in the SD （ smooth and discontinuous systems） oscillator was studied with the gener- alized cell mapping digraph method （GCMD）. Based on the global analysis of the SD oscillator, we found the road to chaos was due to the collision of the period attractor and the chaotic saddle. Chaotic saddle is the transi- ent self-cycling cell set in the cell state space, after the collision chaotic saddle becomes the new portion of the chaotic attractor. The interior crisis will not change the shape of the basin of attractor, and is invertible and in- sensitive to the excitation. Simultaneously, the generalized cell mapping digraph method was improved, and a new algorithm was advanced to gain the box-counting dimension. |
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| Keywords: | generalized cell mapping digraph method interior crisis saddle box-counting dimension chaotic |
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