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碰撞振动系统中周期轨擦边诱导的混沌激变
  • ISSN号：0459-1879
  • 期刊名称：《力学学报》
  • 时间：0
  • 分类：O322[理学—一般力学与力学基础;理学—力学]
  • 作者机构：[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
  • 相关基金：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
作者： 冯进钤[1], 徐伟[2]
关键词： 碰撞振动系统, 擦边流形, 擦边诱导激变, 图胞映射方法, vibro-impact system, grazing manifold, grazing-induced crisis, digraph cell mapping
中文摘要：

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Duffing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．

英文摘要：

A numerical approximation of grazing manifold is proposed via the digraph cell mapping method. The global dynamics of grazing-induced crisis for a typical Dufting 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.

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期刊信息
  • 《力学学报》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国力学学会 中国科学院力学研究所
  • 主编：魏悦广
  • 地址：北京市海淀区北四环西路15号中科院力学所内《力学学报》
  • 邮编：100190
  • 邮箱：lxxb@cstam.org.cn
  • 电话：010-62536271
  • 国际标准刊号：ISSN：0459-1879
  • 国内统一刊号：ISSN：11-2062/O3
  • 邮发代号:2-814
  • 获奖情况:
  • 1992年首届自然科技期刊一等奖,1996年国家自然科技期刊二等奖,2000年首届国家期刊奖
  • 国内外数据库收录:
  • 美国数学评论（网络版）,荷兰文摘与引文数据库,美国工程索引,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:13332