Chaotic and non-chaotic responses in a class of stochastic Hamiltonian systems
The noise-contaminated dynamics in a class of Hamiltonian systems under stochastic excitation was studied. The necessary condition for noise-induced chaos could be readily derived from the stochastic Melnikov method. However, some current quantitive methods were emphasized on identifying the noise-contaminated sample responses in such system.As an illustrating example, the Duffing oscillator under parametrically harmonic and external bounded-noise excitations was studied in detail, from which one can learn nothing about the system noise-contaminated dynamics from the stochastic Melnikov condition. Safe basins and sample responses of the system were then simulated with the Monte-Carlo and Runge-Kutta methods, from which the leading Lyapunov exponents by using the Rosenstein algorithm and the correlation dimensions due to the PPS algorithm from Small, et al. were shown to characterize the dynamical nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal when the system is excited by the external bounded-noise. Most importantly, the noisy harmonic, the noise-induced chaotic and the random-predominant responses can be identified when one adjusts the parameter values.
Chun-biao Gan Xiao-yin Cheng
Institute of Applied Mechanics, SAA, Zhejiang University, Hangzhou 310027, China Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong, China
国际会议
The 5th International Conference on Nonlinear Mechanics(第五届国际非线性力学会议)
上海
英文
1240-1254
2007-06-11（万方平台首次上网日期，不代表论文的发表时间）