Noisy Chaos in a Quasi-integrable Hamiltonian System with Two DOF under harmonic and Bounded noise excitations
Noisy Chaos in a Quasi-integrable Hamiltonian System with Two DOF under harmonic and Bounded noise excitations
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DOI：
10.1142/s0218127412501179
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
C. Gan;Y. H. Wang;S. X. Yang;H. Lei
中科院分区：
文献类型：
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作者：
C. Gan;Y. H. Wang;S. X. Yang;H. Lei
本文给出了随机拟可积Hamilton系统的高维Melnikov方法的一种推广形式。以一个具有两个自由度的拟可积Hamilton系统为例，详细推导了系统在简谐和有界噪声激励下的随机Melnikov过程，并给出了混沌发生的均方判据.结果表明，通过改变有界噪声的确定性强度，可以调节混沌运动发生的阈值，通过研究阈值区域的变化，可以找到与有界噪声激励带宽有关的参数范围，在该范围内混沌运动更容易发生.根据扩展的随机Melnikov方法的均方准则，选取一些参数来模拟系统的样本响应，然后计算最大李雅普诺夫指数来识别这些样本响应。
This paper presents an extended form of the high-dimensional Melnikov method for stochastically quasi-integrable Hamiltonian systems. A quasi-integrable Hamiltonian system with two degree-of-freedom (DOF) is employed to illustrate this extended approach, from which the stochastic Melnikov process is derived in detail when the harmonic and the bounded noise excitations are imposed on the system, and the mean-square criterion on the onset of chaos is then presented. It is shown that the threshold of the onset of chaos can be adjusted by changing the deterministic intensity of bounded noise, and one can find the range of the parameter related to the bandwidth of the bounded noise excitation where the chaotic motion can arise more readily by investigating the changes of the threshold region. Furthermore, some parameters are chosen to simulate the sample responses of the system according to the mean-square criterion from the extended stochastic Melnikov method, and the largest Lyapunov exponents are then calculated to identify these sample responses.