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。
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 bi- furcations 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.
出处
《西北工业大学学报》
EI
CAS
CSCD
北大核心
2015年第1期88-92,共5页
Journal of Northwestern Polytechnical University
基金
国家自然科学基金(11472212
11302171)
中央高校基本科研业务费专项资金(3102014JCQ01080)资助
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
bifurcationexponent
Breaking） （ mathematics ）, chaosattractor emerging crisis,theory, differential equations, nonlinear systems,boundary crisis, chaotic saddle, interior crisis,Top LyapunovSB （ Symmetry
