碰撞振动系统中周期轨擦边诱导的混沌激变

冯进钤; 徐伟

doi:10.6052/0459-1879-12-315

碰撞振动系统中周期轨擦边诱导的混沌激变

doi: 10.6052/0459-1879-12-315

冯进钤^1, ,,
徐伟²

1.
西安工程大学理学院, 西安710048
2. 西北工业大学理学院, 西安710072

基金项目: 国家自然科学基金(11172233); 陕西省教育厅专项科研计划(12JK0854) 和西安工程大学博士科研基金(BS1003) 资助项目.

详细信息

通讯作者:
冯进钤

中图分类号: O322
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出版历程
- 收稿日期: 2012-11-09
- 修回日期: 2012-12-18
- 刊出日期: 2013-01-18

GRAZING-INDUCED CHAOSTIC CRISIS FOR PERIODIC ORBITS IN VIBRO-IMPACT SYSTEMS

Feng Jinqian^{1
, ,},
Xu Wei²

1.
School of Science, Xi’an Polytechnic University, Xi’an 710048, China
2. College of Science, Northwestern Polytechnical University, Xi’an 710072, China

Funds: The project was supported by the National Natural Science Foundation of China (11172233), the Scientific Research Program of the Education Bureau of Shanxi Province, China (12JK0854) and the Doctoral Program of Xi’an Polytechnic University, China (BS1003).

摘要

摘要: 基于图胞映射理论, 提出了一种擦边流形的数值逼近方法, 研究了典型Du ng 碰撞振动系统中擦边诱导激变的全局动力学. 研究表明, 周期轨的擦边导致的奇异性使得系统同时产生1 个周期鞍和1 个混沌鞍. 当该周期鞍的稳定流形与不稳定流形发生相切时, 边界激变发生使得该混沌鞍演化为混沌吸引子. 噪声可以诱导周期吸引子发生擦边, 这种擦边导致了1 种内部激变的发生, 表现为该周期吸引子与其吸引盆内部的混沌鞍发生碰撞后演变为1 个混沌吸引子.
- 碰撞振动系统 /
- 擦边流形 /
- 擦边诱导激变 /
- 图胞映射方法
Abstract: A numerical approximation of grazing manifold is proposed via the digraph cell mapping method. The global dynamics of grazing-induced crisis for a typical Du ng vibro-impact system are then investigated. The results reveal that, the singularity caused by the grazing nature of periodic orbits can induce a bifurcation where a periodic saddle and a chaotic saddle arise simultaneously. When the stable and unstable manifolds of the periodic saddle undergo the tangency, a boundary crisis occurs and a chaotic attractor is then brought from the chaotic saddle. Also, grazing phenomenon of periodic orbits induced by noise can be observed. This grazing phenomenon can induce a novel interior crisis, where a chaotic attractor arises due to the collision of this periodic attractor and the chaotic saddle.
- vibro-impact system /
- grazing manifold /
- grazing-induced crisis /
- digraph cell mapping

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参考文献(18)

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