一类含三势阱Mathieu-Duffing振子的相对转动系统的分岔和混沌

摘要

The dynamic equation of a nonlinear relative rotation system with a triple-well Mathieu-Duffing oscillator is inves-tigated. Firstly, a codimension three-bifurcation characteristic is deduced by combining with the multi-scale method and singularity theory under the condition of nonautonomy. Secondly, the threshold value of chaos about Smale horseshoe commutation is given from Melnikov method. Finally, the numerical simulation exhibits safe basins and chaos, and the erosion process of safe basins, which is closely related to the process, leading to chaos.%建立了一类具有三势阱Mathieu-Duffing振子的两质量相对转动系统的非线性动力学方程。应用多尺度法和奇异性理论分析该系统在非自治情况下的余维3分岔特性。利用Melnikov方法获得系统在Smale马蹄意义下混沌的阈值。最后通过数值仿真，研究了系统的混沌行为和安全盆分岔，得到安全盆被侵蚀的过程与系统通向混沌的过程之间密切联系。