用广义胞映射研究参数不确定的多吸引子共存系统<sup>*</sup>

用广义胞映射研究参数不确定的多吸引子共存系统^*

基金项目: 国家自然科学基金资助项目(19672046)

Department of Engineering Mechanics, Xi'an Jiaotong University, Xi'an 710049, P. R. China

摘要: 本文运用广义胞映射对具有参数不确定的多吸引子共存系统进行了分析,指出了参数不确定性对多吸引子共存系统全局特性的影响.并进一步得到可以通过各个吸引子的保护层厚度大小的比较,来判断随着不确定程度的增加,哪一个吸引子将要首先消失.
- 广义胞映射 /
- 多吸引子共存 /
- 参数不确定
Abstract: In this paper the generalized cell mapping(GCM) method is used to study multiple-attractor coexisting system with parameter uncertainties.The effects that the uncertain parameters has on the global properties of the system are presentes.And it is obtained that the attraetor with much smaller value of protect thickness,will disappear firsthy with the degree of the uncertainty of parameter increasing.
- generalized cell mapping /
- multiple-attractor coexisting system /
- parameter uncertainties

[1]	R.Valery Roy Noise.Perturbations of a non-linear system with multiple steady states,Internat.J.Non-Linear Mech.,29,5(1994),755-773.
[2]	Rsingh and C.Lee,Frequency response of linear systems with parameter uncertaintics,J.Sound Vibration,168(1993),71-92.
[3]	C.S.Hsu,A generalized theory of cell-to-cell mapping for nonlinear dynamical systems,J.Applied Mechanics,48(1981),634-642.
[4]	C.S.Hsu,Cell-to-Cell Mapping,A Method of Global Analysis for Nonlinear Systems,Springer-Verlag,New York(1987).
[5]	C.S.Hsu.and H.M.Chiu,Global analysis of a system with multiple responses including a strange attractors,J.Sound Vibration,b4(1987),203-218.
[6]	Mohamed S.Solinlan and J.M.T.Thompson,Global dynamics Underlying sharp basin crosion in nonlinear driven osccillators,Physical Review A,45,6(1992),3425-3431.
[7]	C.S.Hsu,Global analysis by cell mapping,International Journal of Bifurcation and Chaos,2,4(1992),727-771.
[8]	Wilfred D.Iwan and Ching-Tung Huang,On the dynamic response of non-linear systems with parameter uncertainties,Internat.J Non-Linear Mech.,31,5(1996),631-645.
[9]	J.Q.Sun and C.S.Hsu,Effects of small random uncertainties on non-linear systems studied by the generalized cell mapping method,J.Sound Vibration,147,2(1991),185-201.
[10]	Steven W.Medonald,Celso Grebogi,Edward Ott and James A.Yorke,Fractal basin boundary,Physica D.,17(1985),125-153.