Singular analysis of bifurcation systems with two parameters

Bifurcation properties of dynamical systems with two parameters are investigated in this paper.The definition of transition set is proposed,and the approach developed is used to investigate the dynamic characteristic of the nonlinear forced Duffing system with nonlinear feedback controller. The whole parametric plane is divided into several persistent regions by the transition set,and then the bifurcation diagrams in different persistent regions are obtained.