一类含Mathieu-Duffing振子的相对转动系统的分岔和混沌

建立了一类具有Mathieu-Duffing振子的两质量相对转动系统的非线性动力学方程. 应用多尺度法求解该系统发生主共振-基本参数共振的分岔响应方程，并通过奇异性分析得到系统稳态响应的转迁集. 利用Melnikov方法讨论系统在外激扰动和参激扰动变化下的全局分岔和系统进入混沌状态的可能途径，得到外激和参激幅值变化下系统可能出现多次通向混沌的道路，获得系统发生混沌的必要条件. 最后采用数值方法验证了理论研究的有效性. 关键词： 相对转动 Mathieu-Duffing振子 混沌 Melnikov方法

Bifurcation and chaos in some relative rotation systems with Mathieu-Duffing oscillator

The dynamic equation of relative rotation nonlinear dynamic system with Mathieu-Duffing oscillator is investigated. Firstly, the bifurcation response align of the relative rotation system under primary resonance-basic parameters condition is deduced using the method of multiple scales, and a singularity analysis is employed to obtain the transition set of steady motion. Secondly, a global bifurcation of the system, some probable routes leading to chaos and multiple times leading to chaos with parametric and external excitation amplitude changes have been discussed by using Melnikov method, and the necessary condition for chaotic motion of the system is presented. Finally, a numerical method is employed to further prove the effectiveness of the theoretical research.
Keywords： relatively rotation Mathieu-Duffing chaos Melnikov method