【作者】 郭云松； 甘春标；

【Author】 Guo Yunsong and Gan Chunbiao (Department of Mechanics, Zhejiang University, Hangzhou, 310027)

【机构】 浙江大学力学系；

【摘要】 本文通过对多样本响应的数值模拟,讨论了有界噪声激励对软弹簧杜芬振子的倍周期分岔及混沌运动的影响。文中首先描绘了系统受侵蚀的安全盆,进而确定进行后继动力学分析的初始点。随后的系统运动的时间历程图、倍周期分岔图以及Lyapunov 指数图等方面的数值结果表明,外加随机激励的作用往往会改变原确定性系统的规则运动及规则的倍周期分岔图,也可使系统内在的随机行为提前发生,即可使系统更容易出现混沌运动。更多还原

【Abstract】 This paper discusses the effects of bounded noise excitation on the period-doubling bifurcation and chaotic motions of the softening Duffing oscillator. Eroded safe basins of the system are firstly given, from which the reasonable initial value is picked up for the subsequent dynamic analysis. The numerical results from the time history, the period-doubling bifurcation and the maximum Lyapunov exponents show that external bounded noise excitation can mask the regular motions of a deterministic system and bring an essential change to the motions of the system: break through the period-doubling bifurcation and make the chaotic motions of the system arise easily.更多还原