Hopf bifurcation of a nonlinear delayed system of machine tool vibration via pseudo-oscillator analysis
Feng Gao, Huailei Wang and Zaihua Wang
Abstract: On the basis of the newly developed pseudo-oscillator analysis, the local dynamics near a Hopf bifurcation of a nonlinear delayed system of machine tool vibration is investigated in this paper. Starting from a pseudo-oscillator that is slightly perturbed from an undamped oscillator, the pseudo-oscillator analysis shows that near the Hopf bifurcation, the local dynamics can be justified simply by the properties of the averaged pseudo-power function. Unlike the widely used approaches such as the center manifold reduction, the pseudo-oscillator analysis involves very easy computation and gives prediction of the local dynamics with high accuracy.
原文链接：https://www.sciencedirect.com/science/article/pii/S1468121806000927
