Abstract Nonsmooth factors widely exist in natural and engineering areas, so it is important to study in general by dynamics theories. For non-smmoth systems, there not only are general bifurcations in smooth systems, but also occur special bifurcations, which are named non-smooth bifurcations. These non-smooth bifurcations have important effect on system dynamic behavior, and provide more routes to chaos. This is hot and difficult point for non-smooth dynamics.