| 一类非光滑映射的边界碰撞分岔 |
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| 引用本文： | 秦志英,李群宏.一类非光滑映射的边界碰撞分岔[J].力学学报,2013,45(1):25-29. |
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| 作者姓名： | 秦志英 李群宏 |
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| 作者单位： | 1. 河北科技大学机械工程学院, 石家庄050018;
2. 广西大学数学与信息科学学院, 南宁530004 |
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| 基金项目： | 国家自然科学基金(11002046,10972059);河北省自然科学基金(A2011208007)资助项目~~ |
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| 摘 要： | 对于一类分段映射讨论了非线性幂次z导致的不同非光滑性, 推导了周期n 解的边界碰撞分岔及光滑flip和fold 分岔条件. 通过数值仿真验证了这些分岔条件的正确性, 发现存在稳定周期窗的加周期分岔序列是非光滑映射的一个普遍现象, 根本原因在于边界碰撞分岔和光滑flip 或fold 分岔相互作用. 当z取值不同分岔序列有很大的不同, 而参数γ 对于分岔序列的结构影响不大, 因此令参数γ=0 可简化映射的参数分析.
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| 关 键 词： | 非光滑 非连续 边界碰撞 分岔条件 分岔序列 |
| 收稿时间： | 2012-11-09 |
| 修稿时间： | 2012-12-14 |
BORDER-COLLISION BIFURCATION IN A KIND OF NON-SMOOTH MAPS |
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| Qin Zhiying,Li Qunhong.BORDER-COLLISION BIFURCATION IN A KIND OF NON-SMOOTH MAPS[J].chinese journal of theoretical and applied mechanics,2013,45(1):25-29. |
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| Authors: | Qin Zhiying Li Qunhong |
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| Institution: | 1. School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China;
2. College of Mathematics and Information Science, Guangxi University, Nanning 530004, China |
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| Abstract: | For a kind of piecewise map, its nonsmoothness with the parameter z is discussed, and the conditions for border-collision bifurcation and smooth flip/fold bifurcation are derived. These bifurcation conditions are verified by numerical simulation, and the period-adding bifurcation scenario is a general phenomenon for non-smooth maps. The bifurcation scenario is rooted on the interrelation between border-collision bifurcation and smooth flip/fold bifurcation. The parameter z has important effect on the bifurcation scenario, but the parameter has a minor effect, so the analysis γ on bifurcation scenarios with parameters can be simplified by giving γ=0. |
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| Keywords: | nonsmooth|discontinuous|border collision|bifurcation conditions|bifurcation scenarios |
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