有界噪声与谐和激励联合作用下Duffing-Rayleigh振子的Melnikov混沌  

Melnikov chaos in Duffing-Rayleigh oscillator subjected to combined bounded noise and harmonic excitations

作　　者：冯俊[1] 徐伟[1] 顾仁财[1] 狄根虎[1] 

机构地区：[1]西北工业大学应用数学系,西安710129

出　　处：《物理学报》2011年第9期170-177,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10872165;10932009)资助的课题~~

摘　　要：研究了有界噪声与谐和激励作用下的Duffing-Rayleigh振子的动力学行为.首先运用随机Melnikov过程方法得到系统出现混沌的条件,结果表明随着非线性阻尼参数的增加系统会从混沌运动到周期运动,随着Wiener过程强度参数的增加,系统由混沌进入周期的临界幅值会先递增后不变.最后,用两类数值方法即最大Lyapunov指数与Poincare截面验证了上述结果.In this paper,the dynamic behavior of Duffing-Rayleigh oscillator subjected to combined bounded noise and harmonic excitations is investigated. Theoretically, the random Melnikov＇s method is used to establish the conditions of existence of chaotic motion. The result implies that the chaotic motion of the system turns into the periodic motion with the increase of nonlinear damping parameter, and the threshold of random excitation amplitude for the system to change from chaotic to periodic motion in the oscillator turns from increasing to constant as the intensity of the noise increases. Numerically,the largest Lyapunov exponents and the Poincare maps are also used for verifying the conclusion.

关 键 词：有界噪声 随机Melnikov过程 混沌运动 周期运动 

分 类 号：O415.5[理学—理论物理]