一类非线性动力系统混沌运动的研究

The Study on the Chaotic Motion of a Nonlinear Dynamic System

讨论了含二次和三次非线性项的受迫振动系统¨Ｔ－λ１Ｔ＋λ２Ｔ２＋λ３Ｔ３＝ε（ｇｃｏｓωｔ－ε′Ｔ）的混沌运动，利用Ｍｅｌｎｉｋｏｖ函数法给出了发生混沌的临界条件，结合相平面轨迹。

In this paper the system of the forced vibration -λ 1T+λ 2T 2+λ 3T 3=ε(g cos ωt-ε′) is discussed, which contains square and cubic items. The critical condition that the system enters chaotic states is given by the Melnikov method. By Poincaré map, phase portrait and time_displacement history diagram, whether the chaos occurs is determined.