分岔参数的分维数识别法

A FRACTIONARY DIMENSION IDENTIFICATION METHOD OF CRITICAL BIFURCATED PARAMETERS

广泛用于各行各业的转子系统的稳定性问题一直倍受关注。而在当今失稳多是由于一些非线性现象的出现所引起，这就对转子系统的设计提出了更高的要求：考虑非线性因素，避开会出现非线性现象的不稳定参数点或区域。本文中通过对一经典倍周期分岔模型—Ｍａｙ 模型及单盘Ｊｅｆｆｃｏｔｔ转子的研究，得出了利用随参数变化的时间序列分维数趋势图。

The nonlinear behaviors of rotor systems set high requirements to the designing of motor system:Such as to take nonlinear elements into account;to avoid the unstable parameter points or regions where will appear nonlinear phenomena.For this purpose,from studying a typical fractional model-May model and Jeffcott rotor system,the map of the fractional dimension of time-serial vs the parameter is obtained,which can identify critical bifurcated parameters of nonlinear dynamical system quite well.