有界噪声激励下典型非线性系统响应的最大Lyapunov指数估计  

Estimation on the Leading Lyapunov Exponent of the Response in a Typical Nonlinear System under the Bounded Noise Excitation

作　　者：谢潮涌[1] 雷华[1] 甘春标[2] 

机构地区：[1]浙江大学航空航天学院应用力学研究所,杭州310027 [2]浙江大学机械工程学系,杭州310027

出　　处：《噪声与振动控制》2011年第2期7-11,共5页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(10672140)

摘　　要：讨论有界噪声激励对一类典型非线性系统的动力学行为的影响。通过Monte-Carlo和小数据量方法,给出Holmes型杜芬振子在受周期激励和有界噪声激励作用下的样本响应及其最大Lyapunov指数结果。分析表明,在系统有确定性激励作用的导向时,可以由最大Lyapunov指数来判断系统运动是否混沌,且可得出推断:随机激励可诱发混沌亦可抑制混沌。然而,在系统仅受有界噪声激励时,难以从响应曲线和最大Lyapunov指数结果来判别系统的运动是否是混沌的。In this paper,the influence of the bounded noise excitation on the dynamical behaviors in a typical nonlinear oscillatory system is discussed.By using the Monte-Carlo method and small data sets method,the results of the system＇s noise responses and their corresponding leading Lyapunov exponents are presented when the Holmes-type Duffing oscillator is subjected to the bounded noise excitation.It is shown that the leading Lyapunov exponent can be employed to identify chaos when the system is oriented by the determinatc harmonic excitation,from which it can be deduced that the bounded noise excitation can induce or suppress chaos.However,it is difficult to identify chaos from the sample responses and the leading Lyapunov exponents when the system is excited by bounded noise excitation only.

关 键 词：声学 有界噪声 相空间重构 小数据量法 最大LYAPUNOV指数 混沌 

分 类 号：O324[理学—一般力学与力学基础] O175[理学—力学]