有界噪声激励下非线性系统吸引子的关联维数估计

随机环境下非线性系统的动力学分析是一个复杂而又困难的问题,此时系统响应的随机特性可来自测试误差、系统自身的非线性特点或动力学噪声等因素。讨论了有界噪声对两种不同参数的Holmes型杜芬振子的动力学行为的影响。通过Monte-Carlo和相空间重构方法,给出了此两种模型在受周期激励、有界噪声激励作用下的样本时间序列以及样本响应的关联维数结果。分析表明,外加有界噪声的作用可使系统响应的关联维数增大。

ESTIMATION OF CORRELATION DIMENSIONS OF NONLINEAR SYSTEMS UNDER BOUNDED-NOISE EXCITATION

Noise-contaminated dynamic analysis is a complex and difficult topic in nonlinear systems under stochastic background. The random behavior of such systems’ responses may come from measure error, nonlinearity or dynamic noise, etc. The effects of bounded-noise excitation on the Duffing oscillator of Holmes type are discussed. Using the Monte-Carlo method and phase space reconstruction skill, the simulation results of system’s responses and their corresponding correlation dimensions are presented when the parameters in the system assume two different sets of values. It is shown that the presence of external bounded-noise excitation leads to an increase in the correlation dimension of different attractors.