Generalized Hopf Bifurcation for Non-smooth Planar Dynamical Systems： the Corner Case
摘要
Piece-wise smooth systems are an important class of ordinary differential equations whosedynamics are known to exhibit complex bifurcation scenarios and chaos. Broadly speaking,piece-wise smooth systems can undergo all the bifurcation that smooth ones can. Moreinterestingly, there is a whole class of bifurcation that are unique to piece-wise smoothsystems, such as the bifurcation caused by the geometric shape of the region in which thevector field is analyzed. For example (see Figure 1), the region is divided into two partsI and Ⅱ by a discontinuity boundary which contains a corner at O. When an orbit crossthe corner, border-collision bifurcation may occur (cf. [1]). The present paper deals withthe mechanics of the generalized Hopf bifurcation when the stationary point locates at thecorner.